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Hardy–Stein identity for pure-jump Dirichlet forms

Volume 71 / 2023

Michał Gutowski Bulletin Polish Acad. Sci. Math. 71 (2023), 65-84 MSC: Primary 31C25; Secondary 42B25, 60J35, 60G51. DOI: 10.4064/ba230404-1-6 Published online: 26 June 2023


We prove the $L^p$ variant of the Hardy–Stein identity for Sobolev–Bregman forms associated with pure-jump Dirichlet forms with killing, under rather mild assumptions. Along the way, we obtain a general result in terms of the $p$-form defined in a more abstract way.


  • Michał GutowskiFaculty of Pure and Applied Mathematics
    Wrocław University of Science and Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland
    ORCID: 0000-0002-7294-4778

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