Hardy–Stein identities and square functions for semigroups

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 Lp two‐way boundedness, for 1

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Bibliographic Details
Published in:Journal of the London Mathematical Society 2016-10, Vol.94 (2), p.462-478
Main Authors: Bañuelos, Rodrigo, Bogdan, Krzysztof, Luks, Tomasz
Format: Article
Language:English
Subjects:
Analysis of PDEs
Functional Analysis
Mathematics
Probability
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Description
Summary: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 Lp two‐way boundedness, for 1
ISSN:0024-6107
1469-7750
DOI:10.1112/jlms/jdw042