Sharp weighted bounds for fractional integral operators in a space of homogeneous type

Details Sharp weighted bounds for fractional integral operators in a space of homogeneous type Sharp weighted bounds for fractional integral operators in a space of homogeneous type

2012-02-29

arxiv.org/abs/1202.6587v1

Mathematics

Classical Analysis and ODEs

16 pages

Scientific paper

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. We investigate the dependence of the operator norm on weighted spaces on the weight constant, and find the sharp relationship between these two quantities. Our result generalizes the resent Euclidean result by Lacey, Moen, P\'erez and Torres [9].

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