Infimal convolution and Muckenhoupt A p (.) condition in variable L p spaces期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Infimal convolution and Muckenhoupt A _{p (.)} condition in variable L ^p spaces

Authors:	Tengizi S. Kopaliani

Affiliation:	(1) Department of Mechanics and Mathematics, Tbilisi State University, 1 Chavchavadze Ave., Tbilisi, 380028, Georgia

Abstract:	We study the Hardy-Littlewood maximal operator M on $L^{p(.)}({mathbb{R}}^{n})$ . Under the assumptions that the exponent p satisfies and is constant outside some large ball, we prove that $M : L^{p(.)}(mathbb{R}^{n}) longrightarrow L^{p(.)}(mathbb{R}^{n})$ if and only if $dx in A_{p}(.)$ . Received: 2 June 2006 Revised: 28 November 2006

Keywords:	Primary: 42B20 42B45
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