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

OSVALDO GOROSITO; ANA MARÍA KANASHIRO; GLADIS GUADALUPE PRADOLINI

ACTA MATHEMATICA HUNGARICA

SPRINGER

Lugar: Budapest; Año: 2015 vol. 147 p. 354 - 367

0236-5294

In this article 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 cite{K} and, as a consequence, Stein´s result in cite{S} turns out to be true in more general contexts.