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arXiv · 1506.01208

Martingale transforms and the Hardy-Littlewood-Sobolev inequality for semigroups

Daesung Kim
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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 $g$-function.

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Daesung Kim. 2015-06-03. Martingale transforms and the Hardy-Littlewood-Sobolev inequality for semigroups. https://arxiv.org/abs/1506.01208

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