Abstract
We give a characterization of reverse type inequalities on weighted Orlicz spaces of the generalized maximal operator \({M_{\eta}}\), associated to a Young function \({\eta}\), 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.
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The first and second author are supported by Universidad Nacional del Litoral.
The third author is supported by Consejo Nacional de Investigaciones Científicas y Técnicas de la República Argentina and Universidad Nacional del Litoral.
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Gorosito, O., kanashiro, A.M. & Pradolini, G. Characterizations of reverse weighted inequalities for maximal operators in Orlicz spaces and Stein’s result. Acta Math. Hungar. 147, 354–367 (2015). https://doi.org/10.1007/s10474-015-0528-3
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DOI: https://doi.org/10.1007/s10474-015-0528-3