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

Authors: AIGERIM KALYBAY, RYSKUL OINAROV

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.

Keywords: Integral operator, kernel, weighted Lebesgue space, weighted Sobolev space, boundedness, compactnes

Full Text: PDF