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Journal of Function Spaces
Volume 2015, Article ID 581064, 5 pages
http://dx.doi.org/10.1155/2015/581064
Research Article

A Local Estimate for the Maximal Function in Lebesgue Spaces with EXP-Type Exponents

1Dipartimento di Architettura, Università di Napoli, Via Monteoliveto 3, 80134 Napoli, Italy
2Istituto per le Applicazioni del Calcolo “Mauro Picone”, Sezione di Napoli, Consiglio Nazionale delle Ricerche, Via Pietro Castellino 111, 80131 Napoli, Italy

Received 18 March 2015; Accepted 3 May 2015

Academic Editor: Henryk Hudzik

Copyright © 2015 Alberto Fiorenza. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

It is proven that if in a bounded domain and if for some , then given , the Hardy-Littlewood maximal function of , , is such that . Because , the thesis is slightly weaker than for some . The assumption that for some is proven to be optimal in the framework of the Orlicz spaces to obtain in the same class of spaces.