Weighted boundedness of fractional integrals associated with admissible functions on spaces of homogeneous type

Let \(({{\mathcal {X}}},d,\mu )\) $(\mathcal{X},d,\mu )$ be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, we first establish several weighted norm estimates for various maximal functions. Then we show the weighted boundedness of the fractional integral \(I_\beta \) $I_{\beta }$ associated with admissible functions and its commutators. Similarly to \(I_\beta \) $I_{\beta }$ , corresponding results for Calderón–Zygmund operators T associated with admissible functions are also included in this article.