Archiv der Mathematik

, Volume 89, Issue 2, pp 185–192 | Cite as

Infimal convolution and Muckenhoupt Ap(.) condition in variable Lp spaces

Article

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 \(dx \in A_{p}(.)\) .

Mathematics Subject Classification (2000).

Primary: 42B20, 42B45 

Keywords.

Hardy-Littlewood maximal operator variable Lp spaces infimal convolution 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  1. 1.Department of Mechanics and MathematicsTbilisi State UniversityTbilisiGeorgia

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