Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 23-50

GENERALIZED MAXIMAL FUNCTIONS AND RELATED OPERATORS ON WEIGHTED MUSIELAK-ORLICZ SPACES

Ana Bernardis, Estefanía Dalmasso and Gladis Pradolini

Facultad de Ingeniería Química, Universidad Nacional del Litoral (UNL)
and Instituto de Matemática Aplicada del Litoral, CONICET - UNL
Güemes 3450, 3000 Santa Fe, Argentina; bernard 'at' santafe-conicet.gov.ar

Facultad de Ingeniería Química, Universidad Nacional del Litoral (UNL)
and Instituto de Matemática Aplicada del Litoral, CONICET - UNL
Güemes 3450, 3000 Santa Fe, Argentina; edalmasso 'at' santafe-conicet.gov.ar

Facultad de Ingeniería Química, Universidad Nacional del Litoral (UNL)
and Instituto de Matemática Aplicada del Litoral, CONICET - UNL
Güemes 3450, 3000 Santa Fe, Argentina; gpradolini 'at' santafe-conicet.gov.ar

Abstract. 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.

2010 Mathematics Subject Classification: Primary 42B25.

Key words: Musielak-Orlicz spaces, weights, maximal functions.

Reference to this article: A. Bernardis, E. Dalmasso and G. Pradolini: Generalized maximal functions and related operators on weighted Musielak-Orlicz spaces. Ann. Acad. Sci. Fenn. Math. 39 (2014), 23-50.

Full document as PDF file

doi:10.5186/aasfm.2014.3904