Kernel operators and their boundedness from weighted Sobolev space to weighted Lebesgue space

Abstract

In this paper, for a wide class of integral operators, we consider the problem of their boundedness from aweighted Sobolev space to a weighted Lebesgue space. The crucial step in the proof of the main result is to use theequivalence of the basic inequality and certain Hardy-type inequality, so we first state and prove this equivalence.