Boundedness of Littlewood-Paley operators in generalized Orlicz-Campanato spaces
type: Item
instance of: scholarly article
title: Boundedness of Littlewood-Paley operators in generalized Orlicz-Campanato spaces
zbMATH Open document ID: 1196.42021
DOI: 10.1216/RMJ-2010-40-4-1355
published in: Rocky Mountain Journal of Mathematics
publication date: 2010-09-07T00:00:00Z
review text: One knows that the Littlewood-Paley \(g\)-function \(g(f)\), Lusin area function \(S(f)\) and the Stein's function \(g_{\lambda}^{*}(f)\) are bounded on \(L^p({\mathbb R}^n)\). \textit{D. S. Kurtz} [Proc. Am. Math. Soc. 99, 657--666 (1987; Zbl 0658.42022)] and \textit{S. Wang} [Ill. J. Math. 33, No. 4, 531--541 (1989; Zbl 0671.42018)] proved the boundedness on BMO and Lipschitz spaces. The authors obtain the boundedness of these operators on generalized Orlicz-Campanato spaces \({L}^{\Phi, \phi}({\mathbb R}^n)\) where \(\Phi\) and \(\phi\) satisfy appropriate conditions.
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 42B35
zbMATH DE Number: 5779832
zbMATH Keywords: Littlewood-Paley \(g\)-function
zbMATH Keywords: Lusin area integral
zbMATH Keywords: Orilicz-Campanato space
author: Songyan Zhang
author: Xiangxing Tao
reviewed by: Yasuo Komori-Furuya
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5779832