Hardy-Stein identities and square functions for semigroups

Rodrigo Bañuelos (1) , Krzysztof Bogdan (2) , Tomasz Luks (3)

1 Department of mathematics Purdue University
2 Wroclaw University of Science and Technology
3 I2M - Institut de Mathématiques de Marseille

We prove a Hardy-Stein type identity for the semigroups of symmetric, pure-jump L\'evy processes. Combined with the Burkholder-Gundy inequalities, it gives the $L^p$ two-way boundedness, for $1

Mots clés: LITTLEWOOD-PALEY INEQUALITY; BROWNIAN-MOTION; LEVY PROCESSES; TRANSFORM

Domaines: Analyse fonctionnelle [math.FA]; Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]

Rodrigo Bañuelos, Krzysztof Bogdan, Tomasz Luks. Hardy-Stein identities and square functions for semigroups. Journal of the London Mathematical Society, 2015, 94 (2), pp.462 - 478. ⟨10.1112/jlms/jdw042⟩. ⟨hal-01485175⟩