Two-Weight Norm Estimates for Multilinear Fractional Integrals in Classical Lebesgue Spaces

We derive criteria governing two-weight estimates for multilinear fractional integrals and appropriate maximal functions. The two and one weight problems for multi(sub)linear strong fractional maximal operators are also studied; in particular, we derive necessary and sufficient conditions guaranteeing the trace type inequality for this operator. We also establish the Fefferman-Stein type inequality, and obtain one-weight criteria when a weight function is of product type. As a consequence, appropriate results for multilinear Riesz potential operator with product kernels follow.

Rough Multilinear Fractional Integrals on Weighted Morrey Spaces

It is showed that a class of multilinear fractional operators with rough kernels, which are similar to the higher-order commutators for the rough fractional integrals, are bounded on the weighted Morrey spaces.