Generalized maximal functions and related operators on weighted Musielak-Orlicz spaces

BERNARDIS, ANA; DALMASSO, ESTEFANÍA; PRADOLINI, GLADIS

ANNALES ACADEMIAE SCIENTIARUM FENNICAE. MATHEMATICA

SUOMALAINEN TIEDEAKATEMIA

Lugar: Helsinki; Año: 2014 vol. 39 p. 23 - 50

1239-629X

We characterize the class of weights related to the boundedness of maximal operators associated to a Young function $eta$ in the context of variable Lebesgue spaces. Fractional versions of these results are also obtained by means of a weighted Hedberg type inequality. These results are new even in the classical Lebesgue spaces. We also deal with Wiener´s type inequalities for the mentioned operators in the variable context. As applications of the strong type results for the maximal operators, we derive weighted boundedness properties for a large class of operators controlled by them.