Boundedness of the potential operators and their commutators in the local “complementary” generalized variable exponent Morrey spaces on unbounded sets

Autor:	Aykol, Canay, Badalov, Xayyam A., Hasanov, Javanshir J.
Zdroj:	Annals of Functional Analysis; 20240101, Issue: Preprints p1-16, 16p
Abstrakt:	In this paper we prove a Sobolev–Spanne type ?M{x0}p(·),?(O)??M{x0}q(·),?(O)-theorem for the potential operators Ia, where ?M{x0}p(·),?(O)is local “complementary” generalized Morrey spaces with variable exponent p(x), ?(r)is a general function defining the Morrey-type norm and Ois an open unbounded subset of Rn. In addition, we prove the boundedness of the commutator of potential operators [b,Ia]in these spaces. In all cases the conditions for the boundedness are given in terms of Zygmund-type integral inequalities on ?(x,r), which do not assume any assumption on monotonicity of ?(x,r)in r.
Databáze:	Supplemental Index
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