Weighted Bergman projections and tangential area integrals

William Cohn

Studia Mathematica (1993)

  • Volume: 106, Issue: 1, page 59-76
  • ISSN: 0039-3223

Abstract

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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 k p ( ∂ 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 k p ( ∂ Ω ) .

How to cite

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Cohn, William. "Weighted Bergman projections and tangential area integrals." Studia Mathematica 106.1 (1993): 59-76. <http://eudml.org/doc/216003>.

@article{Cohn1993,
abstract = {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 $H^p_k(∂Ω)$.},
author = {Cohn, William},
journal = {Studia Mathematica},
keywords = {weighted Bergman projection; Hardy-Sobolev space},
language = {eng},
number = {1},
pages = {59-76},
title = {Weighted Bergman projections and tangential area integrals},
url = {http://eudml.org/doc/216003},
volume = {106},
year = {1993},
}

TY - JOUR
AU - Cohn, William
TI - Weighted Bergman projections and tangential area integrals
JO - Studia Mathematica
PY - 1993
VL - 106
IS - 1
SP - 59
EP - 76
AB - 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 $H^p_k(∂Ω)$.
LA - eng
KW - weighted Bergman projection; Hardy-Sobolev space
UR - http://eudml.org/doc/216003
ER -

References

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  2. [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. Zbl0601.32007
  3. [AS1] P. Ahern and R. Schneider, Holomorphic Lipschitz functions in pseudoconvex domains, Amer. J. Math. 101 (1979), 543-565. Zbl0455.32008
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  8. [GK] I. Gohberg and N. Krupnik, Einführung in die Theorie der eindimensionalen singulären Integraloperatoren, Birkhäuser, Basel 1979. Zbl0413.47040
  9. [Gr] S. Grellier, Complex tangential characterizations of Hardy-Sobolev spaces of holomorphic functions, preprint. Zbl0779.32001
  10. [KSt] N. Kerzman and E. M. Stein, The Szegö kernel in terms of Cauchy-Fantappiè kernels, Duke Math. J. 45 (1978), 197-223. Zbl0387.32009
  11. [L] E. Ligocka, On the Forelli-Rudin construction and weighted Bergman projections, Studia Math. 94 (1989), 257-272. Zbl0688.32020
  12. [Ra] M. Range, Holomorphic Functions and Integral Representations in Several Complex Variables, Springer, New York 1986. Zbl0591.32002
  13. [Ru] W. Rudin, Function Theory in the Unit Ball of ℂ n , Springer, New York 1980. 
  14. [St1] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton 1970. 
  15. [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. 
  16. [St3] E. M. Stein, Boundary Behavior of Holomorphic Functions of Several Complex Variables, Math. Notes, Princeton Univ. Press, Princeton 1972. 

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