Characterization of Lipschitz functions via the commutators of singular and fractional integral operators in variable Lebesgue spaces

GLADIS PRADOLINI; RAMOS WILFREDO ARIEL

Cordoba

Congreso; XIII Encuentro Nacional de Analistas A. P. Calderón; 2016

We obtain characterizations of a variable version of Lipschitz functionsin terms of the boundedness of commutators of Calderón-Zygmund and fractional type operators, in the context of the variable exponent Lebesgue spaces L(p(.)), where the Lipschitz function is the symbol of the commutator. A usefull tool is a pointwise estimate involving the sharp maximal operator of the commutator with Lipschitz symbol with certain maximal operators in connection with the commutator, which is new even in the classical context. We also prove some boundedness properties of the commutators between Lebesgue and Lipschitz spaces in the variable context.