Potential operators and their commutators acting between variable Lebesgue spaces with different weights

Abstract

We prove that a generalized Fefferman–Phong type conditions on a pair of weights u and v is sufficient for the boundedness of the potential type operator from Lv p(.) into Lu q(.). We also obtain an analogous estimates for their commutators with BMO symbols. We include some estimates for a generalized maximal operator in the variable context Ms(·), and its fractional version, Mβ(·),s(·), between variable versions of L log L type spaces, where S(·) and Mβ(·) are exponents belonging to certain classes.