Hardy-Stein identities and square functions for semigroups

2015/06/30 by Rodrigo Bañuelos, Bañuelos, Rodrigo, Krzysztof Bogdan +3 · 1 citation
Mathematics · #42B15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Primary 42B25 #Probability (math.PR) #Secondary 60J75 #math.AP #math.FA #math.PR #msc:42B15 #msc:42B25 #msc:60J75

paper · pdf · doi:10.48550/arxiv.1506.09007

17 pages

arxiv created 2015/06/30 · arxiv updated 2015/07/01

Abstract

We prove a Hardy-Stein type identity for the semigroups of symmetric, pure-jump Lévy processes. Combined with the Burkholder-Gundy inequalities, it gives the L^p two-way boundedness, for 1<p<∞, of the corresponding Littlewood-Paley square function. The square function yields a direct proof of the L^p boundedness of Fourier multipliers obtained by transforms of martingales of Lévy processes.

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• Littlewood--Paley estimates for pure-jump Dirichlet forms

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