Commutators of Singular Integrals with Kernels Satisfying Generalized Hörmander Conditions and Extrapolation Results to the Variable Exponent Spaces

Abstract

We obtain boundedness results for the higher order commutators of singular integral operators between weighted Lebesgue spaces, including Lp-BMO and Lp-Lipschitz estimates. The kernels of such operators satisfy certain regularity condition, and the symbol of the commutator belongs to a Lipschitz class. We also deal with commutators of singular integral operators with less regular kernels satisfying a Hörmander’s type inequality. Moreover, we give a characterization result involving symbols of the commutators and continuity results for extreme values of p. Finally, by extrapolation techniques, we derive different results in the variable exponent context.