Weighted estimates for generalized maximal operators on Musielak-Orlicz spaces

ANA BERNARDIS; ESTEFANÍA DALMASSO; GLADIS PRADOLINI

Barcelona

Conferencia; International Conference on Function Spaces and Variable Exponent Analysis; 2011

Centre de Recerca Matemàtica-Universidad Autónoma de Barcelona

We prove weighted modular and norm inequalities for a generalized maximal operator related to a submultiplicative Young function in the context of Muzielak-Orlicz spaces. The results extend those obtained by Carlos Pére and by D. Cruz Uribe for the Hardy-Littlewood maximal operator. For the associated fractional maximal function, some estimates are also obtained  by using a pointwise inequality, interesting in itself, which relates both maximal operators.