Martingale transforms and the Hardy-Littlewood-Sobolev inequality for semigroups
Probability
2015-06-04 v1
Abstract
We give a representation of the fractional integral for symmetric Markovian semigroups as the projection of martingale transforms and prove the Hardy-Littlewood-Sobolev(HLS) inequality based on this representation. The proof rests on a new inequality for a fractional Littlewood-Paley -function.
Keywords
Cite
@article{arxiv.1506.01208,
title = {Martingale transforms and the Hardy-Littlewood-Sobolev inequality for semigroups},
author = {Daesung Kim},
journal= {arXiv preprint arXiv:1506.01208},
year = {2015}
}
Comments
13 pages