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Volumn 48, Issue 2, 2004, Pages 251-307

Carleson's Theorem: Proof, complements, variations

Author keywords

Fourier series; Phase plane analysis; Pointwise convergence; Singular integrals

Indexed keywords


EID: 10044297117     PISSN: 02141493     EISSN: None     Source Type: Journal    
DOI: 10.5565/PUBLMAT_48204_01     Document Type: Review
Times cited : (34)

References (91)
  • 1
    • 0000531215 scopus 로고    scopus 로고
    • Convergence of Fourier series
    • Proceedings of the, XX Workshop on Function Theory (Moscow, 1995)
    • N. YU. ANTONOV, Convergence of Fourier series, in: "Proceedings of the, XX Workshop on Function Theory" (Moscow, 1995), East J. Approx. 2(2) (1996), 187-190.
    • (1996) East J. Approx. , vol.2 , Issue.2 , pp. 187-190
    • Antonov, N.Y.U.1
  • 2
    • 78049238552 scopus 로고    scopus 로고
    • Pointwise convergence of Fourier series
    • Springer-Verlag, Berlin
    • J. ARIAS DE REYNA, ''Pointwise convergence of Fourier series", Lecture Notes in Mathematics 1785, Springer-Verlag, Berlin, 2002.
    • (2002) Lecture Notes in Mathematics , vol.1785
    • Arias De Reyna, J.1
  • 3
    • 0036333885 scopus 로고    scopus 로고
    • Pointwise convergence of Fourier series
    • J. ARIAS DE REYNA. Pointwise convergence of Fourier series. J. London Math. Soc. (2) 65(1) (2002), 139-153.
    • (2002) J. London Math. Soc. (2) , vol.65 , Issue.1 , pp. 139-153
    • Arias De Reyna, J.1
  • 4
    • 10044228803 scopus 로고
    • A special trigonometric series and its applications, (Russian)
    • 2
    • G. I. ARKHIPOV AND K. I. OSKOLKOV. A special trigonometric series and its applications, (Russian). Mat. Sb. (N.S.) 134(176). no. 2 (1987), 147-157. 287: translation in Math. USSR-Sb. 62(1) (1989). 145-155.
    • (1987) Mat. Sb. (N.S.) , vol.134 , Issue.176 , pp. 147-157
    • Arkhipov, G.I.1    Oskolkov, K.I.2
  • 5
    • 0009222489 scopus 로고
    • G. I. ARKHIPOV AND K. I. OSKOLKOV. A special trigonometric series and its applications, (Russian). Mat. Sb. (N.S.) 134(176). no. 2 (1987), 147-157. 287: translation in Math. USSR-Sb. 62(1) (1989). 145-155.
    • (1989) Math. USSR-Sb. , vol.62 , Issue.1 , pp. 145-155
  • 6
    • 84966209912 scopus 로고
    • The helical transform as a connection between ergodic theory and harmonic analysis
    • I. ASSANI AND K. PETERSEN, The helical transform as a connection between ergodic theory and harmonic analysis. Trans. Amer. Math. Soc. 331(1) (1992), 131-142.
    • (1992) Trans. Amer. Math. Soc. , vol.331 , Issue.1 , pp. 131-142
    • Assani, I.1    Petersen, K.2
  • 7
    • 0040827322 scopus 로고
    • Some connections between ergodic theory and harmonic analysis
    • Evanston, IL, 1989. Academic Press, Boston, MA
    • I. ASSANI, K. PETERSEN AND H. WHITE. Some connections between ergodic theory and harmonic analysis, in: "Almost everywhere convergence. II" (Evanston, IL, 1989). Academic Press, Boston, MA, 1991, pp. 17-40.
    • (1991) Almost Everywhere Convergence II , vol.2 , pp. 17-40
    • Assani, I.1    Petersen, K.2    White, H.3
  • 9
    • 0038401080 scopus 로고    scopus 로고
    • A weak-type orthogonality principle
    • electronic
    • J. BARRIONUEVO ANDM. T. LACEY. A weak-type orthogonality principle. Proc. Amer. Math. Soc. 131(6) (2003), 1763-1769 (electronic).
    • (2003) Proc. Amer. Math. Soc. , vol.131 , Issue.6 , pp. 1763-1769
    • Barrionuevo, J.1    Lacey, M.T.2
  • 10
    • 0001272904 scopus 로고
    • 2(0,1)
    • 2(0,1), Studia Math. 28 (1966/1967), 363-388.
    • (1966) Studia Math , vol.28 , pp. 363-388
    • Billard, P.1
  • 11
    • 0009408323 scopus 로고
    • A remark on the maximal function associated to an analytic vector field
    • Urbana, IL
    • J. BOURGAIN, A remark on the maximal function associated to an analytic vector field, in: "Analysis at Urbana, Vol. I" (Urbana, IL, 1986-1987), London Math. Soc. Lecture Note Ser. 137, Cambridge Univ. Press, Cambridge, 1989, pp. 111-132.
    • (1986) Analysis at Urbana, Vol. I , vol.1
    • Bourgain, J.1
  • 12
    • 0003395274 scopus 로고
    • Cambridge Univ. Press, Cambridge
    • J. BOURGAIN, A remark on the maximal function associated to an analytic vector field, in: "Analysis at Urbana, Vol. I" (Urbana, IL, 1986-1987), London Math. Soc. Lecture Note Ser. 137, Cambridge Univ. Press, Cambridge, 1989, pp. 111-132.
    • (1989) London Math. Soc. Lecture Note Ser. , vol.137 , pp. 111-132
  • 13
    • 0001732722 scopus 로고
    • Ergodic theory and translation-invariant operators
    • A.-P. CALDERÓN, Ergodic theory and translation-invariant operators, Proc. Nat. Acad. Sci. U.S.A. 59 (1968), 349-353.
    • (1968) Proc. Nat. Acad. Sci. U.S.A , vol.59 , pp. 349-353
    • Calderón, A.-P.1
  • 14
    • 84966216326 scopus 로고
    • The spectral measure and Hilbert transform of a measure-preserving transformation
    • J. CAMPRELL AND K. PETERSEN, The spectral measure and Hilbert transform of a measure-preserving transformation, Trans. Amer. Math. Soc. 313(1) (1989), 121-129.
    • (1989) Trans. Amer. Math. Soc. , vol.313 , Issue.1 , pp. 121-129
    • Camprell, J.1    Petersen, K.2
  • 15
    • 29244464836 scopus 로고    scopus 로고
    • Classes of singular integral operators along variable lines
    • A. CARBERY, A. SEEGER, S. WAINGER AND J. WRIGHT, Classes of singular integral operators along variable lines, J. Geom. Anal. 9(4) (1999), 583-605.
    • (1999) J. Geom. Anal. , vol.9 , Issue.4 , pp. 583-605
    • Carbery, A.1    Seeger, A.2    Wainger, S.3    Wright, J.4
  • 16
    • 0001498106 scopus 로고
    • On convergence and growth of partial sumas of Fourier series
    • L. CARLESON, On convergence and growth of partial sumas of Fourier series, Acta Math. 116 (1966), 135-157.
    • (1966) Acta Math. , vol.116 , pp. 135-157
    • Carleson, L.1
  • 17
    • 0035255585 scopus 로고    scopus 로고
    • WKB asymptotic behavior of almost all generalized eigenfunctions for one-dimensional Schrödinger operators with slowly decaying potentials
    • M. CHRIST AND A. KISELEV, WKB asymptotic behavior of almost all generalized eigenfunctions for one-dimensional Schrödinger operators with slowly decaying potentials, J. Fund. Anal. 179(2) (2001), 426-447.
    • (2001) J. Fund. Anal. , vol.179 , Issue.2 , pp. 426-447
    • Christ, M.1    Kiselev, A.2
  • 18
    • 0036991106 scopus 로고    scopus 로고
    • Scattering and wave operators for one-dimensional Schrödinger operators with slowly decaying non-smooth potentials
    • M. CHRIST AND A. KISELEV, Scattering and wave operators for one-dimensional Schrödinger operators with slowly decaying non-smooth potentials, Geom. Fund. Anal. 12(6) (2002), 1174-1234.
    • (2002) Geom. Fund. Anal. , vol.12 , Issue.6 , pp. 1174-1234
    • Christ, M.1    Kiselev, A.2
  • 19
    • 0035531899 scopus 로고    scopus 로고
    • WKB and spectral analysis of one-dimensional Schrödinger operators with slowly varying potentials
    • M. CHRIST AND A. KISELEV, WKB and spectral analysis of one-dimensional Schrödinger operators with slowly varying potentials, Comm. Math. Phys. 218(2) (2001), 245-262.
    • (2001) Comm. Math. Phys. , vol.218 , Issue.2 , pp. 245-262
    • Christ, M.1    Kiselev, A.2
  • 20
    • 0035255579 scopus 로고    scopus 로고
    • Maximal functions associated to filtrations
    • M. CHRIST AND A. KISELEV, Maximal functions associated to filtrations, J. Fund. Anal. 179(2) (2001), 409-425.
    • (2001) J. Fund. Anal. , vol.179 , Issue.2 , pp. 409-425
    • Christ, M.1    Kiselev, A.2
  • 21
    • 10044226479 scopus 로고    scopus 로고
    • One-dimensional Schr̈dinger operators with slowly decaying potentials: Spectra and asymptotics (or: Baby Fourier analysis meets toy quantum mechanics)
    • University of Arkansas Spring Lecture Series
    • M. CHRIST AND A. KISELEV, One-dimensional Schr̈dinger operators with slowly decaying potentials: spectra and asymptotics (or: Baby Fourier analysis meets toy quantum mechanics), Lecture Notes, University of Arkansas Spring Lecture Series (2002).
    • (2002) Lecture Notes
    • Christ, M.1    Kiselev, A.2
  • 23
    • 1642341339 scopus 로고    scopus 로고
    • Laws of large numbers with rates and the one-sided ergodic Hilbert transform
    • G. COHEN AND M. LIN, Laws of large numbers with rates and the one-sided ergodic Hilbert transform, Illinois J. Math. 47(4) (2003), 997-1031.
    • (2003) Illinois J. Math. , vol.47 , Issue.4 , pp. 997-1031
    • Cohen, G.1    Lin, M.2
  • 24
    • 84968500699 scopus 로고
    • Remarks on weak type inequalities fur operators commuting with translations
    • R. R. COIFMAN, Remarks on weak type inequalities fur operators commuting with translations, Bull. Amer Math. Soc. 74 (1908), 710-714.
    • (1908) Bull. Amer Math. Soc. , vol.74 , pp. 710-714
    • Coifman, R.R.1
  • 25
    • 0017615901 scopus 로고
    • On the equivalence between the boundedness of certain classes of maximal and multiplier operators in Fourier analysis
    • A. CÓRDOBA AND R. FEFFERMAN. On the equivalence between the boundedness of certain classes of maximal and multiplier operators in Fourier analysis. Proc. Nat. Acad. Sci. U.S.A. 74(2) (1977), 423-425.
    • (1977) Proc. Nat. Acad. Sci. U.S.A , vol.74 , Issue.2 , pp. 423-425
    • Córdoba, A.1    Fefferman, R.2
  • 26
    • 1642375260 scopus 로고
    • On random Fourier series
    • J. CUZICK AND TZE LEUNG LAI, on random Fourier series. Trans. Amer. Math. Soc. 261(1) (1980), 53-80.
    • (1980) Trans. Amer. Math. Soc. , vol.261 , Issue.1 , pp. 53-80
    • Cuzick, J.1    Lai, T.L.2
  • 27
    • 0003077036 scopus 로고
    • Ten, lectures on wavelets
    • Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
    • I. DAUBECHIES, "Ten, lectures on wavelets", OBMS-NSF Regional Conference Series in Applied Mathematics 61, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1992.
    • (1992) OBMS-NSF Regional Conference Series in Applied Mathematics , vol.61
    • Daubechies, I.1
  • 28
    • 0000153472 scopus 로고
    • Pointwise convergence of Fourier series
    • C. FEFFERMAN. Pointwise convergence of Fourier series. Ann., of Math. (2) 98 (1973), 551-571.
    • (1973) Ann., of Math. (2) , vol.98 , pp. 551-571
    • Fefferman, C.1
  • 29
    • 84966232487 scopus 로고
    • On the divergence of multiple Fourier series
    • C. FEFFERMAN. On the divergence of multiple Fourier series. Bull. Amer. Math. Soc. 77 (1971), 191-195.
    • (1971) Bull. Amer. Math. Soc. , vol.77 , pp. 191-195
    • Fefferman, C.1
  • 30
    • 84966261827 scopus 로고
    • On the convergence of multiple Fourier series
    • C. FEFFERMAN. On the convergence of multiple Fourier series, Bull. Amer. Math. Soc. 77 (1971), 744-745.
    • (1971) Bull. Amer. Math. Soc. , vol.77 , pp. 744-745
    • Fefferman, C.1
  • 31
    • 0000803776 scopus 로고
    • The multiplier problem for the ball
    • C. FEFFERMAN. The multiplier problem for the ball, Ann. of Math. (2) 94 (1971), 330-336.
    • (1971) Ann. of Math. (2) , vol.94 , pp. 330-336
    • Fefferman, C.1
  • 32
    • 0742323812 scopus 로고    scopus 로고
    • P bounds for a maximal dyadic sum operator
    • P bounds for a maximal dyadic sum operator. Math. Z. 246(1-2) (2004), 321-337.
    • (2004) Math. Z. , vol.246 , Issue.1-2 , pp. 321-337
    • Grafakos, L.1    Tao, T.2    Terwilleger, E.3
  • 33
    • 10044220001 scopus 로고
    • On the summability of Fourier's series
    • G. H. HARDY. On the summability of Fourier's series. J. London Math. Soc. 12 (1913), 305-372.
    • (1913) J. London Math. Soc. , vol.12 , pp. 305-372
    • Hardy, G.H.1
  • 34
    • 0003031805 scopus 로고
    • On the convergence of Fourier series
    • Proc. Oonf., Edwardsville. Ill., Southern Illinois Univ. Press. Carbondale. Ill.
    • R. A. HUNT, On the convergence of Fourier series, in: "1968 Orthogonal Expansions and their Continuous Analogues" (Proc. Oonf., Edwardsville. Ill., 1967), Southern Illinois Univ. Press. Carbondale. Ill., pp. 235-255.
    • (1967) 1968 Orthogonal Expansions and Their Continuous Analogues , pp. 235-255
    • Hunt, R.A.1
  • 35
    • 84968481666 scopus 로고
    • A weighted norm inequality for Fourier series
    • R. A. HUNT AND WO SANG YOUNG. A weighted norm inequality for Fourier series. Bull. Amer. Math. Soc. 80 (1974), 274-277.
    • (1974) Bull. Amer. Math. Soc. , vol.80 , pp. 274-277
    • Hunt, R.A.1    Young, W.S.2
  • 36
    • 0033558669 scopus 로고    scopus 로고
    • Maximal operators over arbitrary sets of directions
    • N. H. KATZ. Maximal operators over arbitrary sets of directions. Duke Math. J. 97(1) (1999), 67-79.
    • (1999) Duke Math. J. , vol.97 , Issue.1 , pp. 67-79
    • Katz, N.H.1
  • 37
    • 10044262399 scopus 로고    scopus 로고
    • A partial result on Lipschitz differentiation
    • South Hadley, MA
    • N. H. KATZ, A partial result on Lipschitz differentiation, in: "Harmonic analysis at Mount Holyoke", (South Hadley, MA, 2001). Contemp. Math. 320. Amer. Math. Soc., Providence. RI, 2003, pp. 217-224.
    • (2001) Harmonic Analysis at Mount Holyoke
    • Katz, N.H.1
  • 38
    • 10044262399 scopus 로고    scopus 로고
    • Amer. Math. Soc., Providence. RI
    • N. H. KATZ, A partial result on Lipschitz differentiation, in: "Harmonic analysis at Mount Holyoke", (South Hadley, MA, 2001). Contemp. Math. 320. Amer. Math. Soc., Providence. RI, 2003, pp. 217-224.
    • (2003) Contemp. Math. , vol.320 , pp. 217-224
  • 39
    • 0000610153 scopus 로고
    • Une série de Fourier-Lebesque divergente presque partout
    • A. N. KOLMOGOROV. Une série de Fourier-Lebesque divergente presque partout. Fund. Math. 4 (1923), 324-328.
    • (1923) Fund. Math. , vol.4 , pp. 324-328
    • Kolmogorov, A.N.1
  • 40
    • 0000504108 scopus 로고
    • Une série de Fourier-Lebesquc diveigente presque partout
    • A. N. KOLMOGOROV, Une série de Fourier-Lebesquc diveigente presque partout, C. R. Acad. Sci. Paris Sér. I Math. 183 (1920). 1327-1329.
    • (1920) C. R. Acad. Sci. Paris Sér. I Math. , vol.183 , pp. 1327-1329
    • Kolmogorov, A.N.1
  • 41
    • 0009908897 scopus 로고    scopus 로고
    • On the divergence everywhere of trigonometric Fourier series, (Russian)
    • S. V. KONYAGIN, On the divergence everywhere of trigonometric Fourier series, (Russian), Mat. Sb. 191(1) (2000), 103-126; translation in 56. Math. 191(1-2) (2000), 97-120.
    • (2000) Mat. Sb. , vol.191 , Issue.1 , pp. 103-126
    • Konyagin, S.V.1
  • 42
    • 10044240894 scopus 로고    scopus 로고
    • S. V. KONYAGIN, On the divergence everywhere of trigonometric Fourier series, (Russian), Mat. Sb. 191(1) (2000), 103-126; translation in 56. Math. 191(1-2) (2000), 97-120.
    • (2000) 56. Math. , vol.191 , Issue.1-2 , pp. 97-120
  • 43
    • 0033569283 scopus 로고    scopus 로고
    • On divergence of trigonometric Fourier series everywhere
    • S. V. KONYAGIN, On divergence of trigonometric Fourier series everywhere, C. R. Acad. Sci. Paris Sér. I Math. 329(8) (1999), 693-697.
    • (1999) C. R. Acad. Sci. Paris Sér. I Math. , vol.329 , Issue.8 , pp. 693-697
    • Konyagin, S.V.1
  • 44
    • 0000843976 scopus 로고
    • Everywhere divergent Fourier series
    • T. W. KÖRNER. Everywhere divergent Fourier series, Colloq. Math. 45(1) (1981), 103-118 (1982).
    • (1981) Colloq. Math. , vol.45 , Issue.1 , pp. 103-118
    • Körner, T.W.1
  • 45
    • 10044279660 scopus 로고
    • Transferring the Carleson-Hunt theorem in the setting of Orlicz spaces
    • Columbia. MO.
    • M. T. LACEY, Transferring the Carleson-Hunt theorem in the setting of Orlicz spaces, in: "Interaction between functional analysis, harmonic analysis, and probability'' (Columbia. MO. 1994), Lecture Notes in Pure and Appl. Math. 175, Dekker, New York. 1996, pp. 307-314.
    • (1994) Interaction between Functional Analysis, Harmonic Analysis, and Probability
    • Lacey, M.T.1
  • 46
    • 0004271690 scopus 로고    scopus 로고
    • Dekker, New York
    • M. T. LACEY, Transferring the Carleson-Hunt theorem in the setting of Orlicz spaces, in: "Interaction between functional analysis, harmonic analysis, and probability'' (Columbia. MO. 1994), Lecture Notes in Pure and Appl. Math. 175, Dekker, New York. 1996, pp. 307-314.
    • (1996) Lecture Notes in Pure and Appl. Math. , vol.175 , pp. 307-314
  • 48
    • 0038544980 scopus 로고    scopus 로고
    • electronic
    • M. T. LACEY, On the bilinear Hubert transform, in: ''Proceedings of the International Congress of Mathematicians. Vol. II" (Berlin, 1998), Doc. Math. Extra Vol. II (1998), 647-656 (electronic).
    • (1998) Doc. Math. , vol.2 EXTRA VOL. , pp. 647-656
  • 49
    • 0036444333 scopus 로고    scopus 로고
    • Carleson's theorem with quadratic phase functions
    • M. T. LACEY, Carleson's theorem with quadratic phase functions. Studia Math. 153(3) (2002), 249-267.
    • (2002) Studia Math. , vol.153 , Issue.3 , pp. 249-267
    • Lacey, M.T.1
  • 53
    • 0001283252 scopus 로고    scopus 로고
    • P estimates on the bilinear Hubert transform for 2 < p < ∞
    • P estimates on the bilinear Hubert transform for 2 < p < ∞, Ann. of Math. (2) 146(3) (1997), 693-724.
    • (1997) Ann. of Math. (2) , vol.146 , Issue.3 , pp. 693-724
    • Lacey, M.T.1    Thiele, C.M.2
  • 54
    • 0032574820 scopus 로고    scopus 로고
    • On Calderón's conjecture for the bilinear Hilbert transform
    • electronic
    • M. T. LACEY AND C. M. THIELE, On Calderón's conjecture for the bilinear Hilbert transform, Proc. Natl. Acad. Sci. USA 95(9) (1998), 4828-4830 (electronic).
    • (1998) Proc. Natl. Acad. Sci. USA , vol.95 , Issue.9 , pp. 4828-4830
    • Lacey, M.T.1    Thiele, C.M.2
  • 55
    • 0033416840 scopus 로고    scopus 로고
    • On Calderón's conjecture
    • M. T. LACEY AND C. M. THIELE, On Calderón's conjecture. Ann. of Math, (2) 149(2) (1999), 475-496.
    • (1999) Ann. of Math, (2) , vol.149 , Issue.2 , pp. 475-496
    • Lacey, M.T.1    Thiele, C.M.2
  • 56
    • 0034348701 scopus 로고    scopus 로고
    • A proof of boundedness of the Carleson operator
    • M. T. LACEY AND C. M. THIELE, A proof of boundedness of the Carleson operator, Math. Res. Lett. 7(4) (2000), 361-370.
    • (2000) Math. Res. Lett. , vol.7 , Issue.4 , pp. 361-370
    • Lacey, M.T.1    Thiele, C.M.2
  • 57
    • 0010885713 scopus 로고
    • Spectre quasi-discret et théorème ergodique de Wiener-Wiatner pour les polynômes
    • E. LESIGNE, Spectre quasi-discret et théorème ergodique de Wiener-Wiatner pour les polynômes, Ergodic Theory Dynam. Systems 13(4) (1993), 767-784.
    • (1993) Ergodic Theory Dynam. Systems , vol.13 , Issue.4 , pp. 767-784
    • Lesigne, E.1
  • 58
    • 84971968079 scopus 로고
    • Un théorème de disjonction de systèmes dynamiques et une généralisation du théorème ergodique de Wiener-Wintner
    • E. LESIGNE, Un théorème de disjonction de systèmes dynamiques et une généralisation du théorème ergodique de Wiener-Wintner, Ergodic Theory Dynam. Systems 10(3) (1990), 513-521.
    • (1990) Ergodic Theory Dynam. Systems , vol.10 , Issue.3 , pp. 513-521
    • Lesigne, E.1
  • 59
    • 0002923964 scopus 로고
    • Sur les fonctions indépendentes
    • J. MARCINKIEWICZ AND A. ZYGMUND. Sur les fonctions indépendentes. Fund. Math. 29 (1937), 60-90.
    • (1937) Fund. Math. , vol.29 , pp. 60-90
    • Marcinkiewicz, J.1    Zygmund, A.2
  • 60
    • 0000735690 scopus 로고
    • Characterizations of almost surely continuous p-stable random Fourier series and strongly stationary processes
    • M. B. MARCUS AND G. PISIER, Characterizations of almost surely continuous p-stable random Fourier series and strongly stationary processes, Acta Math. 152(3-4) (1984), 245-301.
    • (1984) Acta Math. , vol.152 , Issue.3-4 , pp. 245-301
    • Marcus, M.B.1    Pisier, G.2
  • 61
    • 10044251531 scopus 로고
    • Convergence of Fourier series of square integrable functions, (Hungarian, with English summary)
    • A. MÁTÉ, Convergence of Fourier series of square integrable functions, (Hungarian, with English summary). Mat. Lapok 18 (1967), 195-242.
    • (1967) Mat. Lapok , vol.18 , pp. 195-242
    • Máté, A.1
  • 62
    • 0036004363 scopus 로고    scopus 로고
    • Multi-linear operators given by singular multipliers
    • electronic
    • C. MUSCALU, T. TAO AND C. M. THIELE, Multi-linear operators given by singular multipliers, J. Amer. Math. Soc. 15(2) (2002), 469-496 (electronic).
    • (2002) J. Amer. Math. Soc. , vol.15 , Issue.2 , pp. 469-496
    • Muscalu, C.1    Tao, T.2    Thiele, C.M.3
  • 63
    • 0036994348 scopus 로고    scopus 로고
    • A discrete model for the bi-Carleson operator
    • C. MUSCALU, T. TAO AND C. M. THIELE. A discrete model for the bi-Carleson operator. Geom. Fund. Anal 12(6) (2002), 1324-1364.
    • (2002) Geom. Fund. Anal , vol.12 , Issue.6 , pp. 1324-1364
    • Muscalu, C.1    Tao, T.2    Thiele, C.M.3
  • 64
    • 0242308156 scopus 로고    scopus 로고
    • A Carleson theorem for a Cantor group model of the scattering transform
    • C. MUSCALU, T. TAO AND C. M. THIELE. A Carleson theorem for a Cantor group model of the scattering transform. Nonlinearity 16(1) (2003), 219-246.
    • (2003) Nonlinearity , vol.16 , Issue.1 , pp. 219-246
    • Muscalu, C.1    Tao, T.2    Thiele, C.M.3
  • 67
    • 0041412891 scopus 로고    scopus 로고
    • A counterexample to a multilinear endpoint question of Christ and Kiselev
    • C. MUSCALU. T. TAO AND C. M. THIELE. A counterexample to a multilinear endpoint question of Christ and Kiselev. Math. Res. Lett. 10(2-3) (2003), 237-246.
    • (2003) Math. Res. Lett. , vol.10 , Issue.2-3 , pp. 237-246
    • Muscalu, C.1    Tao, T.2    Thiele, C.M.3
  • 68
    • 0032330384 scopus 로고    scopus 로고
    • Schrödinger equation and oscillatory Hilbert transforms of second degree
    • K. I. OSKOLKOV, Schrödinger equation and oscillatory Hilbert transforms of second degree, J. Fourier Anal. Appl. 4(3) (1998), 341-356.
    • (1998) J. Fourier Anal. Appl. , vol.4 , Issue.3 , pp. 341-356
    • Oskolkov, K.I.1
  • 69
    • 0002292397 scopus 로고
    • A class of I. M. Vinogradov's series and its applications in harmonic analysis
    • Tampa. FL
    • K. I. OSKOLKOV, A class of I. M. Vinogradov's series and its applications in harmonic analysis, in: ''Progress in approximation theory" (Tampa. FL, 1990). Springer Ser. Comput. Math. 19. Springer, New York. 1992. pp. 353-402.
    • (1990) Progress in Approximation Theory
    • Oskolkov, K.I.1
  • 70
    • 0004209438 scopus 로고
    • Springer, New York.
    • K. I. OSKOLKOV, A class of I. M. Vinogradov's series and its applications in harmonic analysis, in: ''Progress in approximation theory" (Tampa. FL, 1990). Springer Ser. Comput. Math. 19. Springer, New York. 1992. pp. 353-402.
    • (1992) Springer Ser. Comput. Math. , vol.19 , pp. 353-402
  • 71
    • 23044523546 scopus 로고    scopus 로고
    • A Littlewood-Paley inequality for the Carleson operator
    • E. PRESTINI AND P. SJÖLIN, A Littlewood-Paley inequality for the Carleson operator. J. Fourier Anal. Appl. 6(5) (2000), 457-466.
    • (2000) J. Fourier Anal. Appl. , vol.6 , Issue.5 , pp. 457-466
    • Prestini, E.1    Sjölin, P.2
  • 72
    • 0032367056 scopus 로고    scopus 로고
    • The absolutely continuous spectrum of one-dimensional Schrödinger operators with decaying potentials
    • C. REMLING, The absolutely continuous spectrum of one-dimensional Schrödinger operators with decaying potentials. Comm. Math. Phys. 193(1) (1998), 151-170.
    • (1998) Comm. Math. Phys. , vol.193 , Issue.1 , pp. 151-170
    • Remling, C.1
  • 73
    • 0001872538 scopus 로고
    • A Littlewood-Paley inequality for arbitrary intervals
    • J. L. RUBIO DE FRANCIA, A Littlewood-Paley inequality for arbitrary intervals. Rev. Mat. Iberoamericana 1(2) (1985), 1-14.
    • (1985) Rev. Mat. Iberoamericana , vol.1 , Issue.2 , pp. 1-14
    • Rubio De Francia, J.L.1
  • 74
    • 84950356985 scopus 로고
    • An inequality of Paley and convergence a.e. of Walsh-Fourier series
    • 1969
    • P. SJÖLIN, An inequality of Paley and convergence a.e. of Walsh-Fourier series, Ark. Mat. 7 (1969), 551-570 (1969).
    • (1969) Ark. Mat. , vol.7 , pp. 551-570
    • Sjölin, P.1
  • 75
    • 0003043439 scopus 로고
    • Convergence almost everywhere of certain singular integrals and multiple Fourier series
    • P. SJÖLIN. Convergence almost everywhere of certain singular integrals and multiple Fourier series. Ark. Mat. 9 (1971), 65-90.
    • (1971) Ark. Mat. , vol.9 , pp. 65-90
    • Sjölin, P.1
  • 76
    • 0042913567 scopus 로고    scopus 로고
    • Remarks on a theorem by N. Yu. Antonov
    • P. SJÖLIN AND F. SORIA, Remarks on a theorem by N. Yu. Antonov, Studia, Math. 158(1) (2003), 79-97.
    • (2003) Studia, Math. , vol.158 , Issue.1 , pp. 79-97
    • Sjölin, P.1    Soria, F.2
  • 77
    • 0000644687 scopus 로고
    • On limits of seqences of operators
    • E. M. STEIN, On limits of seqences of operators, Ann. of Math. (2) 74 (1961), 140-170.
    • (1961) Ann. of Math. (2) , vol.74 , pp. 140-170
    • Stein, E.M.1
  • 78
    • 0003201639 scopus 로고
    • Singular integrals and differentiability properties of functions
    • Princeton University Press, Princeton, N.J.
    • E. M. STEIN, "Singular integrals and differentiability properties of functions''', Princeton Mathematical Series 30, Princeton University Press, Princeton, N.J., 1970.
    • (1970) Princeton Mathematical Series , vol.30
    • Stein, E.M.1
  • 79
    • 0000298431 scopus 로고
    • Problems in harmonic analysis related to curvature and oscillatory integrals
    • Berkeley, Calif., 1986, Amer. Math. Soc., Providence, RI
    • E. M. STEIN, Problems in harmonic analysis related to curvature and oscillatory integrals, in: "Proceedings of the International Congress of Mathematicians, Vol. 1, 2" (Berkeley, Calif., 1986), Amer. Math. Soc., Providence, RI, 1987, pp. 196-221.
    • (1987) Proceedings of the International Congress of Mathematicians, Vol. 1, 2 , vol.1-2 , pp. 196-221
    • Stein, E.M.1
  • 80
    • 0013476804 scopus 로고
    • Oscillatory integrals related to Radon-like transforms
    • Proceedings of the Conference in Honor of Jean-Pierre Kahane (Orsay, 1993)
    • E. M. STEIN, Oscillatory integrals related to Radon-like transforms, in: "Proceedings of the Conference in Honor of Jean-Pierre Kahane" (Orsay, 1993), J. Fourier Anal. Appl. Special Issue (1995), 535-551.
    • (1995) J. Fourier Anal. Appl. , vol.SPEC. ISSUE , pp. 535-551
    • Stein, E.M.1
  • 81
    • 0003207103 scopus 로고
    • Harmonic analysis: Real-variable methods, orthogonality, and oscillatory integrals
    • Monographs in Harmonic Analysis III, Princeton University Press, Princeton, NJ
    • E. M. STEIN, "Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals", Princeton Mathematical Series 43, Monographs in Harmonic Analysis III, Princeton University Press, Princeton, NJ, 1993.
    • (1993) Princeton Mathematical Series , vol.43
    • Stein, E.M.1
  • 82
    • 0000276005 scopus 로고
    • The estimation of an integral arising in multiplier transformations
    • E. M. STEIN AND S. WAINGER. The estimation of an integral arising in multiplier transformations, Studia Math. 35 (1970), 101-104.
    • (1970) Studia Math. , vol.35 , pp. 101-104
    • Stein, E.M.1    Wainger, S.2
  • 83
    • 0033475015 scopus 로고    scopus 로고
    • 2 estimates for singular Radon transforms
    • 2 estimates for singular Radon transforms. Amer. J. Math. 121(6) (1999), 1291-1336.
    • (1999) Amer. J. Math. , vol.121 , Issue.6 , pp. 1291-1336
    • Stein, E.M.1    Wainger, S.2
  • 84
    • 0001177564 scopus 로고    scopus 로고
    • Discrete analogues in harmonic analysis. II. Fractional integration
    • E. M. STEIN AND S. WAINGER, Discrete analogues in harmonic analysis. II. Fractional integration, J. Anal. Math. 80 (2000), 335-355.
    • (2000) J. Anal. Math. , vol.80 , pp. 335-355
    • Stein, E.M.1    Wainger, S.2
  • 85
    • 0035527921 scopus 로고    scopus 로고
    • Oscillatory integrals related to Carleson's theorem
    • E. M. STEIN AND S. WAINGER, Oscillatory integrals related to Carleson's theorem, Math. Res. Lett. 8(5-6) (2001), 789-800.
    • (2001) Math. Res. Lett. , vol.8 , Issue.5-6 , pp. 789-800
    • Stein, E.M.1    Wainger, S.2
  • 86
    • 10044242048 scopus 로고
    • A borderline random Fourier series
    • M. TALAGRAND, A borderline random Fourier series, Ann. Probab. 23(2) (1995), 776-785.
    • (1995) Ann. Probab. , vol.23 , Issue.2 , pp. 776-785
    • Talagrand, M.1
  • 87
    • 0003733871 scopus 로고    scopus 로고
    • Time-frequency analysis in the discrete phase plane
    • World Sci. Publishing, River Edge, NJ
    • C. M. THIELE, Time-frequency analysis in the discrete phase plane, in: "Topics in analysis and its applications", World Sci. Publishing, River Edge, NJ, 2000, pp. 99-152.
    • (2000) Topics in Analysis and Its Applications , pp. 99-152
    • Thiele, C.M.1
  • 88
    • 23044523527 scopus 로고    scopus 로고
    • The quartile operator and point-wise convergence of Walsh series
    • C. M. THIELE, The quartile operator and point-wise convergence of Walsh series, Trans. Amer. Math. Soc. 352(12) (2000), 5745-5766.
    • (2000) Trans. Amer. Math. Soc. , vol.352 , Issue.12 , pp. 5745-5766
    • Thiele, C.M.1
  • 89
    • 10044294164 scopus 로고    scopus 로고
    • Singular integrals meet modulation invariance
    • Beijing, 2002, Higher Ed. Press, Beijing
    • C. M. THIELE, Singular integrals meet modulation invariance, in: "Proceedings of the International Congress of Mathematicians, Vol. II" (Beijing, 2002), Higher Ed. Press, Beijing, 2002, pp. 721-732.
    • (2002) Proceedings of the International Congress of Mathematicians, Vol. II , vol.2 , pp. 721-732
    • Thiele, C.M.1
  • 90
    • 0040597963 scopus 로고
    • On the ergodic dynamics of almost periodic systems
    • N. WIENER AND A. WINTNER, On the ergodic dynamics of almost periodic systems, Amer. J. Math. 63 (1941), 794-824.
    • (1941) Amer. J. Math. , vol.63 , pp. 794-824
    • Wiener, N.1    Wintner, A.2
  • 91
    • 0004240499 scopus 로고    scopus 로고
    • Cambridge Mathematical Library, Cambridge University Press, Cambridge
    • A. ZYGMUND, "Trigonometric series. Vol. I, II", Third edition, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 2002.
    • (2002) Trigonometric Series. Vol. I, II, Third Edition , vol.1-2
    • Zygmund, A.1


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