Two-weight norm inequalities for product fractional integral operators

Abstract

In the open range 1<p<q<∞, under a certain geometrical condition on weights, two-weight norm inequality for the product fractional integral operator, whose kernel has singularity appeared on each of the coordinate subspaces, is shown to follow from the Fefferman–Phong-type characteristic for the product cubes. This geometrical condition turns out to be the testing condition of Carleson-type embedding for product dyadic cubes.