Weak and strong type estimates for fractional integral operators on Morrey spaces in metric measure spaces

TL;DR

This paper investigates weak and strong type bounds for fractional integral operators acting on Morrey spaces within metric measure spaces, especially when the measure lacks the doubling property, expanding the understanding of these operators in non-standard settings.

Contribution

It provides new weak and strong type estimates for fractional integral operators on Morrey spaces without assuming measure doubling, broadening applicability.

Findings

Established weak and strong type bounds under non-doubling measures.

Extended fractional integral operator theory to more general metric measure spaces.

Enhanced understanding of Morrey space behavior in non-doubling contexts.

Abstract

We discuss here a weak and strong type estimate for fractional integral operators on Morrey spaces, where the underlying measure $\mu$ does not always satisfy the doubling condition.