On the boundedness on inhomogeneous Lipschitz spaces of fractional integrals, singular integrals and hypersingular integrals associated to non-doubling measures on metric spaces

Abstract

In this paper we prove T1 type necessary and sufficient conditions for the boundedness on inhomogeneous Lipschitz spaces of fractional integrals and singular integrals defined on a measure metric space whose measure satisfies a n-dimensional growth. We also show that hypersingular integrals are bounded on these spaces.