Two-weighted estimates for generalized fractional maximal operators on non-homogeneous spaces

Abstract

Let μ be a nonnegative Borel measure on Rd satisfying that μ(Q) ⩽ l(Q)n for every cube Q ⊂ Rn, where l(Q) is the side length of the cube Q and 0 < n ⩽ d. We study the class of pairs of weights related to the boundedness of radial maximal operators of fractional type associated to a Young function B in the context of non-homogeneous spaces related to the measure μ. Our results include two-weighted norm and weak type inequalities and pointwise estimates. Particularly, we give an improvement of a two-weighted result for certain fractional maximal operator proved in W.Wang, C. Tan, Z. Lou (2012).