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1993 | 106 | 1 | 59-76
Tytuł artykułu

Weighted Bergman projections and tangential area integrals

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let Ω be a bounded strictly pseudoconvex domain in $ℂ^n$. In this paper we find sufficient conditions on a function f defined on Ω in order that the weighted Bergman projection $P_{s}f$ belong to the Hardy-Sobolev space $H^p_k(∂Ω)$. The conditions on f we consider are formulated in terms of tent spaces and complex tangential vector fields. If f is holomorphic then these conditions are necessary and sufficient in order that f belong to the Hardy-Sobolev space $H^p_k(∂Ω)$.
Słowa kluczowe
Czasopismo
Rocznik
Tom
106
Numer
1
Strony
59-76
Opis fizyczny
Daty
wydano
1993
otrzymano
1992-06-08
poprawiono
1993-01-25
Twórcy
  • Department of Mathematics, Wayne State University, Detroit, Michigan 48202, U.S.A.
Bibliografia
  • [AB] P. Ahern and J. Bruna, Maximal and area integral characterizations of Hardy-Sobolev spaces in the unit ball of $ℂ^n$, Rev. Mat. Iberoamericana 4 (1988), 123-153.
  • [AN] P. Ahern and A. Nagel, Strong $L^p$ estimates for maximal functions with respect to singular measures; with applications to exceptional sets, Duke Math. J. 53 (1986), 359-393.
  • [AS1] P. Ahern and R. Schneider, Holomorphic Lipschitz functions in pseudoconvex domains, Amer. J. Math. 101 (1979), 543-565.
  • [AS2] P. Ahern and R. Schneider, A smoothing property of the Henkin and Szegö projections, Duke Math. J. 47 (1980), 135-143.
  • [B] F. Beatrous, Boundary estimates for derivatives of harmonic functions, Studia Math. 98 (1991), 55-71.
  • [C] W. Cohn, Tangential characterizations of Hardy-Sobolev spaces, Indiana Univ. Math. J. 40 (1991), 1221-1249.
  • [CMSt] R. Coifman, Y. Meyer and E. Stein, Some new function spaces and their applications to harmonic analysis, J. Funct. Anal. 62 (1985), 304-335.
  • [GK] I. Gohberg and N. Krupnik, Einführung in die Theorie der eindimensionalen singulären Integraloperatoren, Birkhäuser, Basel 1979.
  • [Gr] S. Grellier, Complex tangential characterizations of Hardy-Sobolev spaces of holomorphic functions, preprint.
  • [KSt] N. Kerzman and E. M. Stein, The Szegö kernel in terms of Cauchy-Fantappiè kernels, Duke Math. J. 45 (1978), 197-223.
  • [L] E. Ligocka, On the Forelli-Rudin construction and weighted Bergman projections, Studia Math. 94 (1989), 257-272.
  • [Ra] M. Range, Holomorphic Functions and Integral Representations in Several Complex Variables, Springer, New York 1986.
  • [Ru] W. Rudin, Function Theory in the Unit Ball of $ℂ^n$, Springer, New York 1980.
  • [St1] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton 1970.
  • [St2] E. M. Stein, Some problems in harmonic analysis, in: Harmonic Analysis in Euclidean Spaces, Proc. Sympos. Pure Math. 35, Amer. Math. Soc., 1979, 3-19.
  • [St3] E. M. Stein, Boundary Behavior of Holomorphic Functions of Several Complex Variables, Math. Notes, Princeton Univ. Press, Princeton 1972.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv106i1p59bwm
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