The cauchy-leray integral: Counterexamples to the Lp-theory

Loredana Lanzani; Elias M. Stein

doi:10.1512/iumj.2019.68.7786

The cauchy-leray integral: Counterexamples to the L^p-theory

Loredana Lanzani, Elias M. Stein

Department of Mathematics

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

3 Scopus citations

Abstract

We prove the optimality of the hypotheses guaranteeing the Lp-boundedness for the Cauchy-Leray integral in Cⁿ, n ≥ 2, obtained in [LS-4]. Two domains, both elementary in nature, show that the geometric requirement of strong C-linear convexity, and the regularity of order 2, are both necessary.

Original language	English (US)
Pages (from-to)	1609-1621
Number of pages	13
Journal	Indiana University Mathematics Journal
Volume	68
Issue number	5
DOIs	https://doi.org/10.1512/iumj.2019.68.7786
State	Published - 2019

Keywords

Cauchy Integral
Cauchy-Leray integral
Cauchy-Szego projection
Hardy space
Lebesgue space
Leray-Levi measure
Minimal smoothness
Pseudoconvex domain

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1512/iumj.2019.68.7786

Cite this

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abstract = "We prove the optimality of the hypotheses guaranteeing the Lp-boundedness for the Cauchy-Leray integral in Cn, n ≥ 2, obtained in [LS-4]. Two domains, both elementary in nature, show that the geometric requirement of strong C-linear convexity, and the regularity of order 2, are both necessary.",

keywords = "Cauchy Integral, Cauchy-Leray integral, Cauchy-Szego projection, Hardy space, Lebesgue space, Leray-Levi measure, Minimal smoothness, Pseudoconvex domain",

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