Weighted Weak-type Estimates for Multilinear Commutators of Fractional Integrals on Spaces of Homogeneous Type

Abstract

We obtain weighted distributional inequalities for multilinear commutators of the fractional integral on spaces of homogeneous type. The techniques developed in this work involve the behavior of some fractional maximal functions. In relation to these operators, as a main tool, we prove a weighted weak type boundedness result, which is interesting in itself.