메뉴 건너뛰기




Volumn 1, Issue C, 2001, Pages 195-232

Chapter 5 Λ P -sets in analysis: Results, problems and related aspects

Author keywords

[No Author keywords available]

Indexed keywords


EID: 58149354013     PISSN: 18745849     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1874-5849(01)80007-3     Document Type: Chapter
Times cited : (29)

References (49)
  • 1
    • 0002841764 scopus 로고    scopus 로고
    • A survey of uniqueness questions in multiple trigonometric series
    • Harmonic Analysis and Nonlinear Differential Equations, in honor of V. Shapiro, Amer. Math. Soc.
    • Ash M., and Wang G. A survey of uniqueness questions in multiple trigonometric series. Harmonic Analysis and Nonlinear Differential Equations, in honor of V. Shapiro. Contemporary Math. 208 (1997), Amer. Math. Soc. 35-71
    • (1997) Contemporary Math. , vol.208 , pp. 35-71
    • Ash, M.1    Wang, G.2
  • 2
    • 0034344798 scopus 로고    scopus 로고
    • Some spherical uniqueness theorems for multiple trigonometric series
    • Ash M., and Wang G. Some spherical uniqueness theorems for multiple trigonometric series. Ann. of Math. 151 (2000) 1-33
    • (2000) Ann. of Math. , vol.151 , pp. 1-33
    • Ash, M.1    Wang, G.2
  • 5
    • 84973998065 scopus 로고
    • Squares in arithmetic progressions
    • Bombieri E., Granville A., and Pintz J. Squares in arithmetic progressions. Duke Math. J. 66 3 (1972) 369-385
    • (1972) Duke Math. J. , vol.66 , Issue.3 , pp. 369-385
    • Bombieri, E.1    Granville, A.2    Pintz, J.3
  • 6
    • 0010213180 scopus 로고
    • Sidon sets and Riesz products
    • Bourgain J. Sidon sets and Riesz products. Annales Fourier 35 (1985) 137-148
    • (1985) Annales Fourier , vol.35 , pp. 137-148
    • Bourgain, J.1
  • 7
    • 0000778931 scopus 로고
    • p )-set problem
    • p )-set problem. Acta Math. 162 (1989) 227-245
    • (1989) Acta Math. , vol.162 , pp. 227-245
    • Bourgain, J.1
  • 8
    • 0013511389 scopus 로고
    • On Kolmogorov's rearrangement problem for orthogonal systems and Garsia's conjecture
    • Lindenstrauss J., and Milman V. (Eds), Springer
    • Bourgain J. On Kolmogorov's rearrangement problem for orthogonal systems and Garsia's conjecture. In: Lindenstrauss J., and Milman V. (Eds). GAFA seminar, Lecture Notes in Math.1376 (1989), Springer 209-250
    • (1989) GAFA seminar, Lecture Notes in Math.1376 , pp. 209-250
    • Bourgain, J.1
  • 9
    • 0000420259 scopus 로고
    • Besicovitch type maximal operators and applications to Fourier Analysis
    • Bourgain J. Besicovitch type maximal operators and applications to Fourier Analysis. GAFA 1 2 (1991) 147-187
    • (1991) GAFA , vol.1 , Issue.2 , pp. 147-187
    • Bourgain, J.1
  • 10
    • 84963018923 scopus 로고
    • Eigenfunction bounds for the Laplacian on the n-torus
    • Bourgain J. Eigenfunction bounds for the Laplacian on the n-torus. Intern. Math. Res. Notices 3 (1993) 61-66
    • (1993) Intern. Math. Res. Notices , vol.3 , pp. 61-66
    • Bourgain, J.1
  • 11
    • 34250084341 scopus 로고
    • Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations
    • Bourgain J. Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. GAFA 3 2 (1993) 107-156
    • (1993) GAFA , vol.3 , Issue.2 , pp. 107-156
    • Bourgain, J.1
  • 12
    • 0009303159 scopus 로고
    • Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations
    • Bourgain J. Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. GAFA 3 3 (1993) 209-262
    • (1993) GAFA , vol.3 , Issue.3 , pp. 209-262
    • Bourgain, J.1
  • 13
    • 77956785720 scopus 로고
    • Some new estimates for oscillatory integrals
    • Stein E., Fefferman C., Fefferman R., and Waigner S. (Eds), UP, Princeton
    • Bourgain J. Some new estimates for oscillatory integrals. In: Stein E., Fefferman C., Fefferman R., and Waigner S. (Eds). Essays on Fourier Analysis in honor of (1994), UP, Princeton
    • (1994) Essays on Fourier Analysis in honor of
    • Bourgain, J.1
  • 15
    • 77956782902 scopus 로고
    • On the distribution of Dirichlet sums
    • Bourgain J. On the distribution of Dirichlet sums. J. Analyse Math. 60 (1993) 21-32
    • (1993) J. Analyse Math. , vol.60 , pp. 21-32
    • Bourgain, J.1
  • 16
    • 0000692012 scopus 로고
    • Oscillatory integrals and a multiplier problem for the disc
    • Carleson L., and Söhn P. Oscillatory integrals and a multiplier problem for the disc. Studia Math. 44 (1972) 287-299
    • (1972) Studia Math. , vol.44 , pp. 287-299
    • Carleson, L.1    Söhn, P.2
  • 17
    • 0000152152 scopus 로고
    • Sur les coefficients des séries trigonometriques convergentes sphériquement
    • Connes B. Sur les coefficients des séries trigonometriques convergentes sphériquement. C. R. Acad. Sci. Paris, Sér. A 283 (1976) 159-161
    • (1976) C. R. Acad. Sci. Paris, Sér. A , vol.283 , pp. 159-161
    • Connes, B.1
  • 18
    • 84968520222 scopus 로고
    • A Cantor-Lebesgue theorem in two dimensions
    • Cooke R. A Cantor-Lebesgue theorem in two dimensions. Proc. Amer. Math. Soc. 30 (1971) 547-550
    • (1971) Proc. Amer. Math. Soc. , vol.30 , pp. 547-550
    • Cooke, R.1
  • 20
    • 0000803776 scopus 로고
    • The multiplier problem for the ball
    • Fefferman C. The multiplier problem for the ball. Ann. of Math. 94 (1971) 330-336
    • (1971) Ann. of Math. , vol.94 , pp. 330-336
    • Fefferman, C.1
  • 21
    • 51249187555 scopus 로고
    • A note on spherical summation multipliers
    • Fefferman C. A note on spherical summation multipliers. Israel J. Math. (1973) 44-52
    • (1973) Israel J. Math. , pp. 44-52
    • Fefferman, C.1
  • 22
    • 0002649030 scopus 로고
    • Almost spherical sections of convex bodies
    • Figiel T., Lindenstrauss J., and Milman V. Almost spherical sections of convex bodies. Acta Math. 139 (1977) 53-94
    • (1977) Acta Math. , vol.139 , pp. 53-94
    • Figiel, T.1    Lindenstrauss, J.2    Milman, V.3
  • 23
    • 0003332109 scopus 로고
    • Topics in Almost Everywhere Convergence
    • Maskham Publ. Co, Chicago
    • Garsia A. Topics in Almost Everywhere Convergence. Lectures in Advanced Math. (1970), Maskham Publ. Co, Chicago
    • (1970) Lectures in Advanced Math.
    • Garsia, A.1
  • 24
    • 77956720736 scopus 로고    scopus 로고
    • Seminar Bourbaki
    • March, Soc. Math. de France
    • J. Ginibre, Seminar Bourbaki, March 96, Asterisque, Soc. Math. de France.
    • (1996) Asterisque
    • Ginibre, J.1
  • 25
    • 0032361262 scopus 로고    scopus 로고
    • A new proof of Szemeredi's theorem for arithmetic progressions of length four
    • Gowers W.T. A new proof of Szemeredi's theorem for arithmetic progressions of length four. Geometric and Functional Analysis 8 (1998) 529-551
    • (1998) Geometric and Functional Analysis , vol.8 , pp. 529-551
    • Gowers, W.T.1
  • 26
    • 0003880503 scopus 로고
    • Springer-Verlag, Clarendon, London
    • Halberstam H., and Roth K. Sequences (1983), Springer-Verlag, Clarendon, London
    • (1983) Sequences
    • Halberstam, H.1    Roth, K.2
  • 27
    • 0012957294 scopus 로고
    • A large value estimate for Dirichlet polynomials
    • Heath-Brown D.R. A large value estimate for Dirichlet polynomials. J. London Math. Soc. 2 20 (1979) 8-18
    • (1979) J. London Math. Soc. , vol.2 , Issue.20 , pp. 8-18
    • Heath-Brown, D.R.1
  • 29
    • 0345810412 scopus 로고    scopus 로고
    • Quantum limits on flat tori
    • Jacobson C. Quantum limits on flat tori. Ann. of Math. 145 (1997) 235-266
    • (1997) Ann. of Math. , vol.145 , pp. 235-266
    • Jacobson, C.1
  • 31
    • 0033235846 scopus 로고    scopus 로고
    • Bounds on arithmetic projections, and applications to the Kakeya conjecture
    • Katz N., and Tao T. Bounds on arithmetic projections, and applications to the Kakeya conjecture. Math. Res. Letters 6 (1999) 625-630
    • (1999) Math. Res. Letters , vol.6 , pp. 625-630
    • Katz, N.1    Tao, T.2
  • 32
    • 0003270948 scopus 로고
    • Asymptotic Theory of Finite Dimensional Normed Spaces
    • Springer
    • Milman V., and Schechtman G. Asymptotic Theory of Finite Dimensional Normed Spaces. Lecture Notes in Math. 1200 (1986), Springer
    • (1986) Lecture Notes in Math. , vol.1200
    • Milman, V.1    Schechtman, G.2
  • 33
    • 0003250374 scopus 로고
    • Topics in Multiplicative Number Theorem
    • Springer
    • Montgomery H. Topics in Multiplicative Number Theorem. Lecture Notes in Math. 227 (1971), Springer
    • (1971) Lecture Notes in Math. , vol.227
    • Montgomery, H.1
  • 35
    • 0003248087 scopus 로고
    • Fourier Series with Respect to General Orthogonal Systems
    • Springer, Berlin
    • Olevskii A.M. Fourier Series with Respect to General Orthogonal Systems. Ergebnisse der Math., B. 86 (1975), Springer, Berlin
    • (1975) Ergebnisse der Math., B. , vol.86
    • Olevskii, A.M.1
  • 37
    • 0002106856 scopus 로고
    • Arithmetic characterizations of Sidon sets
    • Pisier G. Arithmetic characterizations of Sidon sets. Bull. Amer. Math. Soc. 8 1 (1993) 87-89
    • (1993) Bull. Amer. Math. Soc. , vol.8 , Issue.1 , pp. 87-89
    • Pisier, G.1
  • 39
    • 0001430981 scopus 로고
    • Trigonometric series with gaps
    • Rudin W. Trigonometric series with gaps. J. Math. Mech. 9 (1960) 103-227
    • (1960) J. Math. Mech. , vol.9 , pp. 103-227
    • Rudin, W.1
  • 40
    • 0002320789 scopus 로고    scopus 로고
    • An infinite Sidon sequence
    • Ruzsa I. An infinite Sidon sequence. J. Number Th. 68 (1998) 63-71
    • (1998) J. Number Th. , vol.68 , pp. 63-71
    • Ruzsa, I.1
  • 41
    • 0001022477 scopus 로고    scopus 로고
    • Oscillatory integrals in Fourier analysis, Beijing Lectures in Harmonic Analysis, E. Stein
    • E. Stein, Oscillatory integrals in Fourier analysis, Beijing Lectures in Harmonic Analysis, E. Stein, Annals of Math. Studies, 112, 305-355
    • Annals of Math. Studies , vol.112 , pp. 305-355
    • Stein, E.1
  • 42
    • 84972553620 scopus 로고
    • Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
    • Strichartz R. Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations. Duke Math. J. 44 (1977) 705-714
    • (1977) Duke Math. J. , vol.44 , pp. 705-714
    • Strichartz, R.1
  • 43
    • 0008293253 scopus 로고
    • Sections of smooth convex bodies via majorizing measures
    • Talagrand M. Sections of smooth convex bodies via majorizing measures. Acta Math. 175 2 (1995) 273-300
    • (1995) Acta Math. , vol.175 , Issue.2 , pp. 273-300
    • Talagrand, M.1
  • 44
    • 0001380081 scopus 로고    scopus 로고
    • The Bochner-Riesz conjecture implies the restriction conjecture
    • Tao T. The Bochner-Riesz conjecture implies the restriction conjecture. Duke Math. J. 96 (1999) 363-376
    • (1999) Duke Math. J. , vol.96 , pp. 363-376
    • Tao, T.1
  • 45
    • 0032343059 scopus 로고    scopus 로고
    • A bilinear approach to the restriction and Kakeya conjectures
    • Tao T., Vargas A., and Vega L. A bilinear approach to the restriction and Kakeya conjectures. J. Amer. Math. Soc. 11 (1998) 967-1000
    • (1998) J. Amer. Math. Soc. , vol.11 , pp. 967-1000
    • Tao, T.1    Vargas, A.2    Vega, L.3
  • 46
    • 84968496791 scopus 로고
    • A restriction theorem for the Fourier transform
    • Tomas P. A restriction theorem for the Fourier transform. Bull. Amer. Math. Soc. 81 (1975) 447-478
    • (1975) Bull. Amer. Math. Soc. , vol.81 , pp. 447-478
    • Tomas, P.1
  • 47
    • 21844498188 scopus 로고
    • An improved bound for Kakeya type maximal functions
    • Wolff T. An improved bound for Kakeya type maximal functions. Revista Math. Iberoamericana 11 (1995) 651-674
    • (1995) Revista Math. Iberoamericana , vol.11 , pp. 651-674
    • Wolff, T.1
  • 48
    • 0002849466 scopus 로고    scopus 로고
    • Recent work connected with the Kakeya problem
    • Amer. Math. Soc., Providence, RI
    • Wolff T. Recent work connected with the Kakeya problem. Prospects in Mathematics (Princeton NJ, 1996) (1999), Amer. Math. Soc., Providence, RI 129-162
    • (1999) Prospects in Mathematics (Princeton NJ, 1996) , pp. 129-162
    • Wolff, T.1
  • 49
    • 0000855641 scopus 로고
    • On Fourier coefficients and transforms of junctions of two variables
    • Zygmund A. On Fourier coefficients and transforms of junctions of two variables. Studia Math. 50 (1974) 189-201
    • (1974) Studia Math. , vol.50 , pp. 189-201
    • Zygmund, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.