Characterizations of reverse weighted inequalities for maximal operators in Orlicz spaces and Stein’s result

We give a characterization of reverse type inequalities on weighted Orlicz spaces of the generalized maximal operator M η , associated to a Young function η , in terms of an appropriated Dini type condition. Our result improves the one given in [ 3 ] and, as a consequence, Stein’s result in [ 10 ] t...

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Bibliographic Details
Published inActa mathematica Hungarica Vol. 147; no. 2; pp. 354 - 367
Main Authors Gorosito, O., kanashiro, A. M., Pradolini, G.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.12.2015
Subjects
Mathematics
Mathematics and Statistics
maximal function
reverse inequality
42B25
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Summary:We give a characterization of reverse type inequalities on weighted Orlicz spaces of the generalized maximal operator M η , associated to a Young function η , in terms of an appropriated Dini type condition. Our result improves the one given in [ 3 ] and, as a consequence, Stein’s result in [ 10 ] turns out to be true in more general contexts.
ISSN:0236-5294
1588-2632
DOI:10.1007/s10474-015-0528-3