In this paper we present several proofs on the extension of M. Riesz fractional integration and di¤erentiation to the contexts of spaces of homogeneous type and measure metric spaces with non-doubling measures. 1. Introduction, some de
nitions, and a basic lemma Professor M. Ash asked me to write a survey article on some of the results that Stephen Vági and I obtained in the nineties on fractio...