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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