Commutators of potential type operators with Lipschitz symbols on variable Lebesgue spaces with different weights

Abstract

We prove that a generalized Fefferman-Phong type condition on a pair of weights uand v is sufficient for the boundedness of the commutators of potential type operators from Lp(·)_v into Lq(·)_u. We also give an improvement of this result in the sense that we not only consider a variable version of power bump conditions, but also weaker norms related to Musielak-Orlicz functions.We consider a wider class of symbols including Lipschitz symbols and some generalizations.