English

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 gg-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}
}

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13 pages