Tangential-exceptional sets for Hardy-Sobolev spaces
type: Item
instance of: scholarly article
title: Tangential-exceptional sets for Hardy-Sobolev spaces
zbMATH Open document ID: 0809.32001
published in: Illinois Journal of Mathematics
publication date: 1995-01-12T00:00:00Z
review text: A characterization of the Hardy-Sobolev spaces \(H^ p_ \alpha\) is obtained in terms of a fractional Cauchy-type transform of functions in \(L^ p (d \sigma)\). As a consequence there are obtained some geometric conditions for a set \(E\) in the unit sphere of \(\mathbb{C}^ n\) to be tangential-exceptional for a function in \(H^ p_ \alpha\), \(\alpha p < n\). For the extreme case \(\alpha p = n\) it is given a necessary condition and some examples which show the accuracy of that condition.
Mathematics Subject Classification ID: 32A40
Mathematics Subject Classification ID: 32A37
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 32H25
zbMATH DE Number: 711025
zbMATH Keywords: tangential approach region
zbMATH Keywords: exceptional sets
zbMATH Keywords: Hardy-Sobolev spaces
author: C. Cascante
author: J. M. Ortega
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 711025