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Volumn 53, Issue 3, 1998, Pages 435-513

Vector-valued Hausdorff-Young inequality and applications

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EID: 0012957773     PISSN: 00360279     EISSN: 14684829     Source Type: Journal    
DOI: 10.1070/RM1998v053n03ABEH000018     Document Type: Article
Times cited : (28)

References (89)
  • 2
    • 51249168238 scopus 로고
    • ;on the distribution of Sidon series"
    • N. H. Asmar and S. Montgomery-Smith, "On the distribution of Sidon series", Ark. Mat. 31 (1993), 13-26.
    • (1993) Ark. Mat. , vol.31 , pp. 13-26
    • Asmar, N.H.1    Montgomery-Smith, S.2
  • 3
    • 0013552416 scopus 로고
    • An inequality in the theory of Fourier integrals
    • K. I. Babenko, "An inequality in the theory of Fourier integrals", Izv. Akad. Nauk SSSR 25 (1961), 531-542.
    • (1961) Izv. Akad. Nauk SSSR , vol.25 , pp. 531-542
    • Babenko, K.I.1
  • 4
    • 0004189013 scopus 로고
    • Fizmatgiz, Moscow
    • N. K. Bari, Trigonometrical series, Fizmatgiz, Moscow 1961; English transl., A treatise on trigonometric series. Vols. I, II, Pergamon Press, New York 1964.
    • (1961) Trigonometrical Series
    • Bari, N.K.1
  • 5
    • 0004210126 scopus 로고
    • English transl., Pergamon Press, New York
    • N. K. Bari, Trigonometrical series, Fizmatgiz, Moscow 1961; English transl., A treatise on trigonometric series. Vols. I, II, Pergamon Press, New York 1964.
    • (1964) A Treatise on Trigonometric Series. , vol.1-2
  • 6
    • 0000898117 scopus 로고
    • Inequalities in Fourier analysis
    • W. Beckner, "Inequalities in Fourier analysis", Ann. of Math. (2) 102 (1975), 159-182.
    • (1975) Ann. of Math. , vol.102 , Issue.2 , pp. 159-182
    • Beckner, W.1
  • 10
    • 0001441033 scopus 로고
    • Theorem of Hardy and Paley for vector-valued analytic functions and related classes of Banach spaces
    • O. Blasco and A. Pelczyński, "Theorem of Hardy and Paley for vector-valued analytic functions and related classes of Banach spaces", Trans. Amer. Math. Soc. 323 (1991), 335-369.
    • (1991) Trans. Amer. Math. Soc. , vol.323 , pp. 335-369
    • Blasco, O.1    Pelczyński, A.2
  • 11
    • 0041022821 scopus 로고
    • On a theorem of M. Riesz on Fourier series
    • R. P. Boas and S. Bochner, "On a theorem of M. Riesz on Fourier series", J. London Math. Soc. 14 (1939), 62-73.
    • (1939) J. London Math. Soc. , vol.14 , pp. 62-73
    • Boas, R.P.1    Bochner, S.2
  • 12
    • 0010249016 scopus 로고
    • Integration von Funktionen, deren Werte die Elemente eines Vektorraumes sind
    • S. Bochner, "Integration von Funktionen, deren Werte die Elemente eines Vektorraumes sind", Fund. Math. 20 (1933), 262-276.
    • (1933) Fund. Math. , vol.20 , pp. 262-276
    • Bochner, S.1
  • 13
    • 84972527102 scopus 로고
    • A Hausdorff-Young inequality for B-convex Banach spaces
    • J. Bourgain, "A Hausdorff-Young inequality for B-convex Banach spaces", J. Pacific Math. 101 (1982), 255-262.
    • (1982) J. Pacific Math. , vol.101 , pp. 255-262
    • Bourgain, J.1
  • 14
    • 0000765075 scopus 로고
    • Vector-valued Hausdorff-Young inequality and applications
    • J. Bourgain, "Vector-valued Hausdorff-Young inequality and applications", Lecture Notes in Math. 1317 (1988), 239-249.
    • (1988) Lecture Notes in Math. , vol.1317 , pp. 239-249
    • Bourgain, J.1
  • 16
    • 0001661294 scopus 로고
    • Indices of function spaces and their relationship to interpolation
    • D. W. Boyd, "Indices of function spaces and their relationship to interpolation", Canad. J. Math. 21 (1969), 1245-1254.
    • (1969) Canad. J. Math. , vol.21 , pp. 1245-1254
    • Boyd, D.W.1
  • 17
    • 0001142946 scopus 로고
    • Intermediate spaces and interpolation, the complex method
    • A. P. Calderón, "Intermediate spaces and interpolation, the complex method", Studio Math. 24 (1964), 113-190.
    • (1964) Studio Math. , vol.24 , pp. 113-190
    • Calderón, A.P.1
  • 18
    • 34250593672 scopus 로고
    • On the existence of certain singular integrals
    • A. P. Calderón and A. Zygmund, "On the existence of certain singular integrals", Acta Math. 88 (1952), 85-139.
    • (1952) Acta Math. , vol.88 , pp. 85-139
    • Calderón, A.P.1    Zygmund, A.2
  • 20
    • 0001923237 scopus 로고
    • Au delà des opérateurs pseudo-différentiels"
    • R. R. Coifman and Y. Meyer, "Au delà des opérateurs pseudo-différentiels", Astérisque 57 (1978), 1-187.
    • (1978) Astérisque , vol.57 , pp. 1-187
    • Coifman, R.R.1    Meyer, Y.2
  • 24
    • 85164654450 scopus 로고
    • Russian transl., Moscow
    • N. Dunford and J. T. Schwartz, Linear operators. Part I: General theory, Interscience Publ. Inc., New York 1958; Russian transl., Izdat. Inostr. Lit., Moscow 1962.
    • (1962) Izdat. Inostr. Lit.
  • 26
    • 0003446044 scopus 로고
    • Academic Press, New York-London
    • p spaces, Academic Press, New York-London 1970.
    • (1970) p Spaces
    • Duren, P.L.1
  • 27
    • 0040428780 scopus 로고
    • Extremal integral representations
    • G. A. Edgar, "Extremal integral representations", J. Funct. Anal. 23 (1976), 145-161.
    • (1976) J. Funct. Anal. , vol.23 , pp. 145-161
    • Edgar, G.A.1
  • 28
    • 84966260607 scopus 로고
    • Characterizations of bounded mean oscillation
    • C. Fefferman, "Characterizations of bounded mean oscillation", Bull. Amer. Math. Soc. 77 (1971), 587-588.
    • (1971) Bull. Amer. Math. Soc. , vol.77 , pp. 587-588
    • Fefferman, C.1
  • 32
    • 0001351104 scopus 로고
    • On a convexity condition in normed linear spaces
    • D. P. Giesy, "On a convexity condition in normed linear spaces", Trans. Amer. Math. Soc. 125 (1966), 114-146.
    • (1966) Trans. Amer. Math. Soc. , vol.125 , pp. 114-146
    • Giesy, D.P.1
  • 35
    • 0001828326 scopus 로고
    • Interpolation of Orlicz spaces
    • J. Gustavsson and J. Peetre, "Interpolation of Orlicz spaces", Studia Math. 60 (1977), 33-59.
    • (1977) Studia Math. , vol.60 , pp. 33-59
    • Gustavsson, J.1    Peetre, J.2
  • 36
    • 0004207439 scopus 로고
    • Van Nostrand, New York
    • P. Halmos, Measure theory, Van Nostrand, New York 1950; Russian transl., Izdat. Inostr. Lit., Moscow 1953.
    • (1950) Measure Theory
    • Halmos, P.1
  • 37
    • 85164654450 scopus 로고
    • Russian transl., Moscow
    • P. Halmos, Measure theory, Van Nostrand, New York 1950; Russian transl., Izdat. Inostr. Lit., Moscow 1953.
    • (1953) Izdat. Inostr. Lit.
  • 39
    • 85164654450 scopus 로고
    • Russian transl. of 1st ed., Moscow
    • G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, 2nd ed., Cambridge Univ. Press, Cambridge 1952; Russian transl. of 1st ed., Izdat. Inostr. Lit., Moscow 1948.
    • (1948) Izdat. Inostr. Lit.
  • 40
    • 0003962321 scopus 로고
    • Springer-Verlag, New York-Berlin
    • E. Hewitt and K. A. Ross, Abstract harmonic analysis, Vols. I, II, Springer-Verlag, New York-Berlin 1970; Russian transl., Nauka, Moscow 1975.
    • (1970) Abstract Harmonic Analysis , vol.1-2
    • Hewitt, E.1    Ross, K.A.2
  • 41
    • 85164649010 scopus 로고
    • Russian transl., Nauka, Moscow
    • E. Hewitt and K. A. Ross, Abstract harmonic analysis, Vols. I, II, Springer-Verlag, New York-Berlin 1970; Russian transl., Nauka, Moscow 1975.
    • (1975)
  • 43
    • 0001017771 scopus 로고
    • Sums of independent Banach space valued random variables
    • J. Hoffman-Jorgensen, "Sums of independent Banach space valued random variables", Studia Math. 52 (1974), 159-186.
    • (1974) Studia Math. , vol.52 , pp. 159-186
    • Hoffman-Jorgensen, J.1
  • 45
    • 0004057553 scopus 로고
    • Springer-Verlag, Berlin-Heidelberg-New York
    • K. Yosida, Functional analysis, 4th ed., Springer-Verlag, Berlin-Heidelberg-New York 1974; Russian transl. of 1st ed, Mir, Moscow 1967.
    • (1974) Functional Analysis, 4th Ed.
    • Yosida, K.1
  • 46
    • 85164635649 scopus 로고
    • Russian transl. of 1st ed, Mir, Moscow
    • K. Yosida, Functional analysis, 4th ed., Springer-Verlag, Berlin-Heidelberg-New York 1974; Russian transl. of 1st ed, Mir, Moscow 1967.
    • (1967)
  • 47
    • 1842780738 scopus 로고
    • Calderón-Zygmund operators, pseudo-differential operators and the Cauchy integral of Calderón
    • J.-L. Journé, "Calderón-Zygmund operators, pseudo-differential operators and the Cauchy integral of Calderón", Lecture Notes in Math. 994 (1983), 1-128.
    • (1983) Lecture Notes in Math. , vol.994 , pp. 1-128
    • Journé, J.-L.1
  • 48
    • 0039444920 scopus 로고
    • On maximal rearrangement inequalities for Fourier transform
    • W. B. Jurkat and G. Sampson, "On maximal rearrangement inequalities for Fourier transform", Trans. Amer. Math. Soc. 282 (1984), 625-643.
    • (1984) Trans. Amer. Math. Soc. , vol.282 , pp. 625-643
    • Jurkat, W.B.1    Sampson, G.2
  • 49
    • 0003851494 scopus 로고
    • D. C. Heath and Co., Lexington, MA Russian transl., Mir, Moscow 1973
    • J. P. Kahane, Some random series of functions, D. C. Heath and Co., Lexington, MA 1968; Russian transl., Mir, Moscow 1973.
    • (1968) Some Random Series of Functions
    • Kahane, J.P.1
  • 50
    • 0004132033 scopus 로고
    • Nauka, Moscow English transi., Pergamon Press, Oxford-Elmsford, NY
    • L. V. Kantorovich and G. P. Akilov, Functional analysis, Nauka, Moscow 1977; English transi., Pergamon Press, Oxford-Elmsford, NY 1982.
    • (1977) Functional Analysis
    • Kantorovich, L.V.1    Akilov, G.P.2
  • 51
    • 0004021698 scopus 로고
    • Nauka, Moscow English transl., Amer. Math. Soc., Providence, RI 1989
    • B. S. Kashin and A. A. Saakyan, Orthogonal series, Nauka, Moscow 1984; English transl., Amer. Math. Soc., Providence, RI 1989.
    • (1984) Orthogonal Series
    • Kashin, B.S.1    Saakyan, A.A.2
  • 52
    • 0007281313 scopus 로고    scopus 로고
    • Estimates of Fourier transforms in Sobolev spaces
    • V. I. Kolyada, "Estimates of Fourier transforms in Sobolev spaces", Studia Math. 125 (1997), 67-74.
    • (1997) Studia Math. , vol.125 , pp. 67-74
    • Kolyada, V.I.1
  • 53
    • 84985316834 scopus 로고
    • On Fourier coefficients of vector-valued functions
    • H. König, "On Fourier coefficients of vector-valued functions", Math. Nachr. 152 (1991), 215-227.
    • (1991) Math. Nachr. , vol.152 , pp. 215-227
    • König, H.1
  • 56
    • 0001528507 scopus 로고
    • Isomorphic characterizations of inner product spaces by orthogonal series with vector-valued coefficients
    • S. Kwapién, "Isomorphic characterizations of inner product spaces by orthogonal series with vector-valued coefficients", Studia Math. 44 (1972), 583-595.
    • (1972) Studia Math. , vol.44 , pp. 583-595
    • Kwapién, S.1
  • 58
    • 0010833447 scopus 로고
    • Une construction d'espaces d'interpolation"
    • J. L. Lions, "Une construction d'espaces d'interpolation", C. R. Acad. Sci. Paris 251 (1960), 1853-1856.
    • (1960) C. R. Acad. Sci. Paris , vol.251 , pp. 1853-1856
    • Lions, J.L.1
  • 60
    • 0002247218 scopus 로고
    • Sur quelques intégrales du type de Dini
    • J. Marcinkiewicz, "Sur quelques intégrales du type de Dini", Ann. Soc. Polon. Math. 17 (1938), 42-50.
    • (1938) Ann. Soc. Polon. Math. , vol.17 , pp. 42-50
    • Marcinkiewicz, J.1
  • 61
    • 0039953354 scopus 로고
    • Type et cotype dans les espaces munis de structures locales inconditionnelles
    • Exposés 24-25, Centre de Math., École Polytech., Paris 1974
    • B. Maurey, "Type et cotype dans les espaces munis de structures locales inconditionnelles", Sem. Maurey-Schwartz (1973-74), Exposés 24-25, Centre de Math., École Polytech., Paris 1974.
    • (1973) Sem. Maurey-Schwartz
    • Maurey, B.1
  • 62
    • 0001921812 scopus 로고
    • Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach
    • B. Maurey and G. Pisier, "Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach", Studia Math. 58 (1976), 45-90.
    • (1976) Studia Math. , vol.58 , pp. 45-90
    • Maurey, B.1    Pisier, G.2
  • 64
    • 84966245127 scopus 로고
    • Fourier type and complex interpolation
    • M. Milman, "Fourier type and complex interpolation", Proc. Amer. Math. Soc. 89 (1983), 246-248.
    • (1983) Proc. Amer. Math. Soc. , vol.89 , pp. 246-248
    • Milman, M.1
  • 65
    • 0013513837 scopus 로고
    • Complex interpolation and geometry of Banach spaces
    • M. Milman, "Complex interpolation and geometry of Banach spaces", Ann. Mat. Pura Appl. 136 (1984), 317-328.
    • (1984) Ann. Mat. Pura Appl. , vol.136 , pp. 317-328
    • Milman, M.1
  • 66
    • 0039836209 scopus 로고
    • A note on rearrangements of Fourier coefficients
    • H. L. Montgomery, "A note on rearrangements of Fourier coefficients", Ann. Inst. Fourier 26:2 (1976), 29-34.
    • (1976) Ann. Inst. Fourier , vol.26 , Issue.2 , pp. 29-34
    • Montgomery, H.L.1
  • 68
    • 0003103421 scopus 로고
    • Sur la transformation de Fourier des fonctions à valeurs vectorielles"
    • J. Peetre, "Sur la transformation de Fourier des fonctions à valeurs vectorielles", Rend. Sem. Mat. Univ. Padova 42 (1969), 15-26.
    • (1969) Rend. Sem. Mat. Univ. Padova , vol.42 , pp. 15-26
    • Peetre, J.1
  • 69
    • 0000943759 scopus 로고
    • Sur l'utilisation des suites inconditionnellement sommables dans la théorie des espaces d'interpolation"
    • J. Peetre, "Sur l'utilisation des suites inconditionnellement sommables dans la théorie des espaces d'interpolation", Rend. Sem. Mat. Univ. Padova 46 (1971-72), 173-190.
    • (1971) Rend. Sem. Mat. Univ. Padova , vol.46 , pp. 173-190
    • Peetre, J.1
  • 70
    • 84968475297 scopus 로고
    • Commensurate sequences of characters
    • A. Pelczyński, "Commensurate sequences of characters", Proc. Amer. Math. Soc. 104 (1988), 525-531.
    • (1988) Proc. Amer. Math. Soc. , vol.104 , pp. 525-531
    • Pelczyński, A.1
  • 71
    • 0002498629 scopus 로고
    • Molecular decompositions and embedding theorems for vector-valued Sobolev spaces with gradient norm
    • A. Pelczyński and M. Wojciechowski, "Molecular decompositions and embedding theorems for vector-valued Sobolev spaces with gradient norm", Studia Math. 107 (1993), 61-100.
    • (1993) Studia Math. , vol.107 , pp. 61-100
    • Pelczyński, A.1    Wojciechowski, M.2
  • 72
    • 4243277928 scopus 로고
    • Les inégalités de Khinchine-Kahane d'après
    • C. Borel", Sémin. géom. des espaces de Banach, Centre de Math., École Polytech., Paris 1978
    • G. Pisier, "Les inégalités de Khinchine-Kahane d'après C. Borel", Sémin. géom. des espaces de Banach, 1977-1978, Exposé VII, Centre de Math., École Polytech., Paris 1978, pp. 1-14.
    • (1977) Exposé , vol.7 , pp. 1-14
    • Pisier, G.1
  • 73
    • 0001266043 scopus 로고
    • Holomorphic semi-groups and the geometry of Banach spaces
    • G. Pisier, "Holomorphic semi-groups and the geometry of Banach spaces", Ann. of Math. (2) 115 (1982), 375-392.
    • (1982) Ann. of Math. , vol.115 , Issue.2 , pp. 375-392
    • Pisier, G.1
  • 74
    • 0003206141 scopus 로고
    • Factorization of linear operators and the geometry of Banach spaces
    • Providence, RI
    • G. Pisier, "Factorization of linear operators and the geometry of Banach spaces", CBMC Reg. Conf. Ser. Math., Amer. Math. Soc., Providence, RI 1986.
    • (1986) CBMC Reg. Conf. Ser. Math., Amer. Math. Soc.
    • Pisier, G.1
  • 75
    • 0004074630 scopus 로고
    • Nauka, Moscow; English transl. of 2nd ed., Gordon and Breach, New York 1966
    • L. S. Pontryagin, Continuous groups, 4th ed., Nauka, Moscow 1984; English transl. of 2nd ed., Gordon and Breach, New York 1966.
    • (1984) Continuous Groups, 4th Ed.
    • Pontryagin, L.S.1
  • 76
    • 0001671364 scopus 로고
    • Martingale and integral transforms of Banach space valued functions
    • J. L. Rubio de Francia, "Martingale and integral transforms of Banach space valued functions", Lecture Notes in Math 1221 (1982), 195-222.
    • (1982) Lecture Notes in Math , vol.1221 , pp. 195-222
    • Rubio De Francia, J.L.1
  • 77
    • 0003136982 scopus 로고
    • Calderon-Zygmund theory for operator-valued kernels
    • J. L. Rubio de Francia, F. J. Ruiz, and J. L. Torrea, "Calderon-Zygmund theory for operator-valued kernels", Adv. Math. 62 (1986), 7-48.
    • (1986) Adv. Math. , vol.62 , pp. 7-48
    • De Francia, J.L.R.1    Ruiz, F.J.2    Torrea, J.L.3
  • 81
    • 84968512827 scopus 로고
    • Fourier series and mean moduli of continuity
    • O. Szasz, "Fourier series and mean moduli of continuity", Trans. Amer. Math. Soc. 42 (1937), 355-395.
    • (1937) Trans. Amer. Math. Soc. , vol.42 , pp. 355-395
    • Szasz, O.1
  • 82
    • 84960579800 scopus 로고
    • A contribution to the theory of Fourier transforms
    • E. C. Titchmarsh, "A contribution to the theory of Fourier transforms", Proc. London Math. Soc. 23 (1924), 279-289.
    • (1924) Proc. London Math. Soc. , vol.23 , pp. 279-289
    • Titchmarsh, E.C.1
  • 86
    • 0001557932 scopus 로고
    • On absolute and uniform convergence of Fourier series
    • P. L. Ul'yanov, "On absolute and uniform convergence of Fourier series", Mat. Sb. 72 (1967), 193-225; English transl. in Math. USSR-Sb. 1 (1967).
    • (1967) Mat. Sb. , vol.72 , pp. 193-225
    • Ul'yanov, P.L.1
  • 87
    • 85164654065 scopus 로고
    • English transl.
    • P. L. Ul'yanov, "On absolute and uniform convergence of Fourier series", Mat. Sb. 72 (1967), 193-225; English transl. in Math. USSR-Sb. 1 (1967).
    • (1967) Math. USSR-Sb. , vol.1
  • 89
    • 0003765696 scopus 로고
    • Cambridge Univ. Press, New York; Russian transl., Mir, Moscow 1965.
    • A. Zygmund, Trigonometrical series, 2nd ed., Vols. I, II, Cambridge Univ. Press, New York 1959; Russian transl., Mir, Moscow 1965.
    • (1959) Trigonometrical Series, 2nd Ed. , vol.1-2
    • Zygmund, A.1


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