Boundedness on inhomogeneous Lipschitz spaces of fractional integrals, singular integrals and hypersingular integrals associated to non-doubling measures

TL;DR

This paper establishes necessary and sufficient conditions for the boundedness of various integral operators on inhomogeneous Lipschitz spaces within non-doubling measure spaces, with extensions and applications in analysis.

Contribution

It provides new

Findings

Characterizes boundedness of fractional, singular, and hypersingular integrals.

Extends results to infinite measure spaces.

Applies findings to real and complex analysis.

Abstract

In the context of a finite measure metric space whose measure satisfies a growth condition, we prove "T1" type necessary and sufficient conditions for the boundedness of fractional integrals, singular integrals, and hypersingular integrals on inhomogeneous Lipschitz spaces. We also indicate how the results can be extended to the case of infinite measure. Finally we show applications to Real and Complex Analysis.