The effect of the smoothness of fractional type operators over their commutators with Lipschitz symbols on weighted spaces

Abstract

We prove boundedness results for integral operators of fractional type and their higher order commutators between weighted spaces, including $L^p$-$L^q$, $L^p$-$BMO$ and $L^p$-Lipschitz estimates. The kernels of such operators satisfy certain size condition and a Lipschitz type regularity, and the symbol of the commutator belongs to a Lipschitz class. We also deal with commutators of fractional type operators with less regular kernels satisfying a Hörmander's type inequality. As far as we know, these last results are new even in the unweighted case. Moreover, we give a characterization result involving symbols of the commutators and continuity results for extreme values of $p$.

References in corpus (1)

• Commutators of singular integrals on generalized $L^p$ spaces with variable exponent

Cited by in corpus (1)

• On two weighted problems for commutators of classical operators with optimal behaviour on the parameters involved and extrapolation results