TY - JOUR AU - Kairema, Anna PY - 2014/05/06 Y2 - 2024/03/29 TI - Sharp Weighted Bounds for Fractional Integral Operators in a Space of Homogeneous Type JF - MATHEMATICA SCANDINAVICA JA - Math. Scand. VL - 114 IS - 2 SE - Articles DO - 10.7146/math.scand.a-17109 UR - https://www.mscand.dk/article/view/17109 SP - 226-253 AB - We consider a version of M. Riesz fractional integral operator on a space of homogeneous type and show an analogue of the well-known Hardy-Littlewood-Sobolev theorem in this context. In our main result, we investigate the dependence of the operator norm on weighted spaces on the weight constant, and find the relationship between these two quantities. It it shown that the estimate obtained is sharp in any given space of homogeneous type with infinitely many points. Our result generalizes the recent Euclidean result by Lacey, Moen, PĂ©rez and Torres [21]. ER -