Pointwise estimate for the Hardy-Littlewood maximal operator on the orbits of contractive mappings

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:395

Article

Aimar, Hugo¹  Carena, Marilina¹ 

[1] Inst Matemat Aplicada Litoral CONICET UNL, Dept Matemat FIQ UNL, Santa Fe, Argentina

关键词: Hardy-Littlewood maximal operator;    Iterated function systems;    Hutchinson orbits;    Muckenhoupt weights;   

DOI  :  10.1016/j.jmaa.2012.05.087

来源: Elsevier

【 摘 要 】

Let M-n denote the Hardy-Littlewood maximal operator on the n-th iteration of a given iterated function system (IFS). We give sufficient conditions on the IFS in order to obtain a pointwise estimate for M-n in terms of the composition of M-0 and a discrete Hardy-Littlewood type maximal operator. As a corollary we prove the uniform preservation of Muckenhoupt condition along the Hutchinson orbits induced by such an IFS. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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