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Martingale Transforms and the Hardy-Littlewood-Sobolev Inequality for Semigroups

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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 the fractional Littlewood-Paley g–function.

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Authors and Affiliations

  1. Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA

    Daesung Kim

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  1. Daesung Kim
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Kim, D. Martingale Transforms and the Hardy-Littlewood-Sobolev Inequality for Semigroups. Potential Anal 45, 795–807 (2016). https://doi.org/10.1007/s11118-016-9571-0

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  • DOI: https://doi.org/10.1007/s11118-016-9571-0

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