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

2017/04/18 by Loredana Lanzani, Elias M. Stein, Lanzani, Loredana +1
Mathematics · #30E20 #31A10 #31B10 #32A25 #32A26 #32A50 #32A55 #42B20 #46E22 #47B34 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:30E20 #msc:31A10 #msc:31B10 #msc:32A25 #msc:32A26 #msc:32A50 #msc:32A55 #msc:42B20 #msc:46E22 #msc:47B34

paper · pdf · doi:10.48550/arxiv.1704.05381

19 pages

arxiv created 2017/04/18 · arxiv updated 2017/04/19

Abstract

The purpose of this paper is to complement the results in [LS-1] by showing the dense definability of the Cauchy-Leray transform for the domains that give the counterexamples of [LS-1], where L^p-boundedness is shown to fail when either the "near" C² boundary regularity, or the strong \mathbb C-linear convexity assumption is dropped.

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