Hardy–Stein identities and square functions for semigroups | Zendy

Bañuelos Rodrigo | Zendy; Bogdan Krzysztof | Zendy; Luks Tomasz | Zendy

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Hardy–Stein identities and square functions for semigroups

Author(s) -

Bañuelos Rodrigo,

Bogdan Krzysztof,

Luks Tomasz

Publication year - 2016

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/jlms/jdw042

Subject(s) - mathematics , square (algebra) , pure mathematics , identity (music) , lévy process , type (biology) , jump , semigroup , function (biology) , martingale (probability theory) , fourier transform , mathematical analysis , philosophy , physics , geometry , ecology , quantum mechanics , evolutionary biology , biology , aesthetics

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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