The \(L^p\) CR Hartogs separate analyticity theorem for convex domains
type: Item
instance of: scholarly article
title: The \(L^p\) CR Hartogs separate analyticity theorem for convex domains
zbMATH Open document ID: 1408.32037
author: Mark G. Lawrence
published in: Mathematische Zeitschrift
publication date: 2018-03-21T00:00:00Z
review text: The author proves an interesting generalization of the classical Hartogs theorem. This theorem states that a function of several complex variables which is separately holomorphic in each variable is continuous and hence holomorphic in its domain of definition. The author considers convex domains \(D\) with a real analytic boundary \(\partial D\), and shows that, under some additional condition on \(\partial D\), an \(L^p\) function \(f\) on \(\partial D\) is CR, and, in consequence, with holomorphic extension to all \(D\), if and only if it has holomorphic extensions on the slices \(\ell\cap D\) for all complex lines \(\ell\) parallel to the coordinate axes. Applications to represent the Szegő kernel as an iterative limit are also given.
Mathematics Subject Classification ID: 32V25
Mathematics Subject Classification ID: 32A35
Mathematics Subject Classification ID: 32A40
zbMATH DE Number: 6851633
zbMATH Keywords: separately holomorphic functions
zbMATH Keywords: CR functions
zbMATH Keywords: Hartogs theorem
zbMATH Keywords: Szegő kernel
MaRDI profile type: Publication
full work available at URL: s00209-017-1894-z
OpenAlex ID: W2613777900
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DOI: 10.1007/S00209-017-1894-Z
description: scientific article; zbMATH DE number 6851633