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

Authors:	Tengizi S Kopaliani

Institution:	(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 $1 < {\rm inf} p \leq {\rm sup} p < \infty$ 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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