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.
KALYBAY, AIGERIM and OINAROV, RYSKUL
"Kernel operators and their boundedness from weighted Sobolev space to weighted Lebesgue space,"
Turkish Journal of Mathematics: Vol. 43:
1, Article 25.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss1/25