A weighted weak type estimate for the fractional integral operator on spaces of homogeneous type

Abstract

Let $(\mathscr{X},\,d,\,\mu)$ be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, we give a sufficient condition on the pair of weights $(u,\,v)$ so that the fractional integral operator on spaces of homogeneous type is bounded from $L^p(\mathscr{X},\,v)$ to weak $L^q(\mathscr{X},\,u)$ with $1<p\leq q<\infty$.