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

2015/06/03 by Daesung Kim, Kim, Daesung
Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR) #Spectral Theory in Mathematical Physics #math.PR

paper · pdf · doi:10.48550/arxiv.1506.01208

13 pages

arxiv created 2015/06/03 · openalex publication_date 2015/06/03 · arxiv updated 2015/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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