Cauchy-Leray-Fantappiè integral in linearly convex domains
type: Item
instance of: scholarly article
title: Cauchy-Leray-Fantappiè integral in linearly convex domains
zbMATH Open document ID: 1304.32002
author: A. S. Rotkevich
published in: Journal of Mathematical Sciences (New York)
publication date: 2014-09-25T00:00:00Z
review text: Let \(\Omega\) be a strictly linearly convex domain with defining function \(\rho\), and let \(dS\) be the measure generated by the form \(\partial\rho\wedge (\overline{\partial}\partial\rho)^{n-1}\). The author proves that the operator \[ K f(z) = \int_{\partial\Omega} \frac{f(\xi)\, dS(\xi)}{\langle\partial\rho(\xi), \xi-z \rangle^n}, \quad z\in\Omega, \] maps \(L^2(\partial\Omega, dS)\) into the Hardy space \(H^2(\Omega)\) defined with respect to \(dS\). Also, he shows that \(K\) and \(K^*\) are bounded on \(\mathrm{BMO}(\partial\Omega)\). The proofs are based on ideas of \textit{T. Hansson} [Ann. Inst. Fourier 49, No. 5, 1477--1501 (1999; Zbl 0944.32004)].
reviewed by: Evgueni Doubtsov
Mathematics Subject Classification ID: 32A26
Mathematics Subject Classification ID: 32A35
Mathematics Subject Classification ID: 32A55
zbMATH DE Number: 6347715
zbMATH Keywords: Cauchy-type kernels
zbMATH Keywords: Hardy spaces
zbMATH Keywords: linearly convex domains
MaRDI profile type: Publication
full work available at URL: s10958-013-1558-4
OpenAlex ID: W2081379685
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DOI: 10.1007/S10958-013-1558-4
description: scientific article; zbMATH DE number 6347715