The Cauchy-Leray integral: counter-examples to the $L^p$-theory

Loredana Lanzani; Elias M. Stein

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arXiv · 1701.03812

The Cauchy-Leray integral: counter-examples to the $L^p$-theory

Loredana Lanzani·Elias M. Stein

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Abstract

We prove the optimality of the hypotheses guaranteeing the $L^p$-boundedness for the Cauchy-Leray integral in $\mathbb C^n$, $n\geq 2$, obtained in [LS-4]. Two domains, both elementary in nature, show that the geometric requirement of strong $\mathbb C$-linear convexity, together with regularity of order 2, are both necessary.

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BibTeX RIS

Loredana Lanzani, Elias M. Stein. 2017-01-13. The Cauchy-Leray integral: counter-examples to the $L^p$-theory. https://arxiv.org/abs/1701.03812

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