Deformations of the \(Z(\omega_2; L(T^m))\) classes
type: Item
instance of: scholarly article
zbMATH Open document ID: 0986.42006
publication date: 2002-01-23T00:00:00Z
Mathematics Subject Classification ID: 42B05
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 41A25
zbMATH DE Number: 1586378
zbMATH Keywords: conjugate function
zbMATH Keywords: Zygmund's condition
zbMATH Keywords: second difference
MaRDI profile type: Publication
author: A. Danelia
title: Deformations of the \(Z(\omega_2; L(T^m))\) classes
published in: Proceedings of A. Razmadze Mathematical Institute
review text: Theorems of I. Privalov and Hardy-Littlewood are well known which state the invariance of \(\text{Lip }\alpha,\) \(0<\alpha<1,\) functions under the conjugation operator, when the \(\alpha\) smoothness is measured in \(C\) or \(L,\) respectively. In the case \(\alpha=1\) such results are no more valid, but Zygmund's result holds in which the second difference is used to define smoothness. In the paper under review the latter result is partially generalized to the multivariate case.
reviewed by: Elijah Liflyand
description: scientific article