Kernel oper ernel operators and their boundedness fr ors and their boundedness from weighted Sobole om 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 a weighted Sobolev space to a weighted Lebesgue space. The crucial step in the proof of the main result is to use the equivalence of the basic inequality and certain Hardy-type inequality, so we first state and prove this equivalence.