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

2017/01/13 by Loredana Lanzani, Elias M. Stein, Lanzani, Loredana +1 · 1 citation
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #math.CV

paper · pdf · doi:10.48550/arxiv.1701.03812

arxiv created 2017/01/13 · arxiv updated 2017/01/17

Abstract

We prove the optimality of the hypotheses guaranteeing the L^p-boundedness for the Cauchy-Leray integral in \mathbb Cⁿ, n≥ 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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• The Cauchy--Szegö Projection for domains in \mathbb Cⁿ with minimal smoothness: weighted theory

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