The role of an integration identity in the analysis of the Cauchy-Leray transform

Loredana Lanzani; Elias M. Stein

doi:10.1007/s11425-017-9115-5

The role of an integration identity in the analysis of the Cauchy-Leray transform

Loredana Lanzani, Elias M. Stein

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

The purpose of this paper is to complement the results by Lanzani and Stein (2017) by showing the dense definability of the Cauchy-Leray transform for the domains that give the counterexamples of Lanzani and Stein (2017), where L^p-boundedness is shown to fail when either the “near” C²boundary regularity, or the strong ℂ-linear convexity assumption is dropped.

Original language	English (US)
Pages (from-to)	1923-1936
Number of pages	14
Journal	Science China Mathematics
Volume	60
Issue number	11
DOIs	https://doi.org/10.1007/s11425-017-9115-5
State	Published - Nov 1 2017

Keywords

Cauchy integral
Cauchy-Szegö projection
Hardy space
Lebesgue space
Leray-Levi measure
minimal smoothness
pseudoconvex domain

ASJC Scopus subject areas

General Mathematics

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10.1007/s11425-017-9115-5

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abstract = "The purpose of this paper is to complement the results by Lanzani and Stein (2017) by showing the dense definability of the Cauchy-Leray transform for the domains that give the counterexamples of Lanzani and Stein (2017), where Lp-boundedness is shown to fail when either the “near” C2boundary regularity, or the strong ℂ-linear convexity assumption is dropped.",

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AB - The purpose of this paper is to complement the results by Lanzani and Stein (2017) by showing the dense definability of the Cauchy-Leray transform for the domains that give the counterexamples of Lanzani and Stein (2017), where Lp-boundedness is shown to fail when either the “near” C2boundary regularity, or the strong ℂ-linear convexity assumption is dropped.

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KW - Cauchy-Szegö projection

KW - Hardy space

KW - Lebesgue space

KW - Leray-Levi measure

KW - minimal smoothness

KW - pseudoconvex domain

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The role of an integration identity in the analysis of the Cauchy-Leray transform

Abstract

Keywords

ASJC Scopus subject areas

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