Hardy-Stein identities and square functions for semigroups

Rodrigo Bañuelos; Krzysztof Bogdan; Tomasz Luks

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arXiv · 1506.09007

Hardy-Stein identities and square functions for semigroups

Rodrigo Bañuelos·Krzysztof Bogdan·Tomasz Luks

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Abstract

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 $1<p<\infty$, 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 L\'evy processes.

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BibTeX RIS

Rodrigo Bañuelos, Krzysztof Bogdan, Tomasz Luks. 2015-06-30. Hardy-Stein identities and square functions for semigroups. https://arxiv.org/abs/1506.09007

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