Exceptional sets for holomorphic Sobolev functions
type: Item
instance of: scholarly article
title: Exceptional sets for holomorphic Sobolev functions
zbMATH Open document ID: 0668.32006
author: Patrick Ahern
published in: Michigan Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: This paper is concerned with the holomorphic function theory of the unit ball \(B^ n\) in \({\mathbb{C}}^ n\). One can define holomorphic Sobolev spaces \(H^ p_{\beta}(B^ n)\) for \(p,\beta >0\) (recently introduced by Beatrous and Burbea). For example, when \(\beta =1\) the space consists of functions in the usual Hardy space \(H^ p(B^ n)\) whose radial derivative (the result of applying the Euler operator) is also in \(H^ p(B^ n)\). The author studies such functions on admissible approach regions towards a boundary point. He demonstrates control over the corresponding maximal function and hence the existence of almost everyhwere admissible limits with respect to any suitable boundary measure. The paper contains careful analysis and a good discussion of the conditions and consequences of the various constructions.
Mathematics Subject Classification ID: 32A35
Mathematics Subject Classification ID: 32A40
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 4093870
zbMATH Keywords: unit ball
zbMATH Keywords: holomorphic Sobolev spaces
zbMATH Keywords: Hardy space
zbMATH Keywords: admissible approach regions
zbMATH Keywords: existence of almost everyhwere admissible limits
zbMATH Keywords: boundary
reviewed by: M. Eastwood
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029003680
OpenAlex ID: W2075339901
DOI: 10.1307/MMJ/1029003680
description: scientific article; zbMATH DE number 4093870