Morrey Spaces and Fractional Integral Operators

TL;DR

This paper investigates the boundedness of fractional integral operators within Morrey spaces on quasimetric measure spaces, establishing key inequalities including Sobolev, trace, and weighted inequalities, with necessary and sufficient conditions under doubling measures.

Contribution

It provides new boundedness criteria for fractional integral operators in Morrey spaces, extending classical results to quasimetric measure spaces with power weights.

Findings

Derived necessary and sufficient conditions for inequalities under doubling measures

Established Sobolev, trace, and weighted inequalities for potential operators

Extended boundedness results to quasimetric measure spaces

Abstract

The present paper is devoted to the boundedness of fractional integral operators in Morrey spaces defined on quasimetric measure spaces. In particular, Sobolev, trace and weighted inequalities with power weights for potential operators are established. In the case when measure satisfies the doubling condition the derived conditions are simultaneously necessary and sufficient for appropriate inequalities.