An exact estimate of the boundary behavior of functions from Hardy-Sobolev classes in the critical case
type: Item
instance of: scholarly article
title: An exact estimate of the boundary behavior of functions from Hardy-Sobolev classes in the critical case
zbMATH Open document ID: 0933.32005
DOI: 10.1007/BF02358977
author: V. G. Krotov
published in: Mathematical Notes
publication date: 2000-04-04T00:00:00Z
review text: The Hardy-Sobolev spaces \(H^p_q(B^n)\) in the unit ball \(B^n \subset\mathbb{C}^n\) is defined as fractional integration of the usual Hardy space \(H_p(B^n)\): \(H^p_q(B^n)= R_q(H^p(B^n)\), where \(R_qf(z)= \Sigma (m+1)^qf_m(z)\) is the operator of the fractional integration. Here \(f(z)= \Sigma f_m(z)\) is the homogeneous expansion of \(f\). If \(pq=n\), the functions from \(H^p_q(B^n)\) have a limit almost everywhere on the boundary along certain regions of exponential contact with the boundary. It is proved that the maximal operator associated with these regions is bounded as an operator from \(H^p_q(B^n)\) to \(L_p(\partial B^n)\).
Mathematics Subject Classification ID: 32A35
Mathematics Subject Classification ID: 32A37
zbMATH DE Number: 1257138
zbMATH Keywords: boundary behavior
zbMATH Keywords: Hardy-Sobolev classes
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1257138