Pré-Publication, Document De Travail Année : 2025

Avatars of Stein's theorem in the complex setting

Résumé

In this paper, we establish some variants of Stein's theorem which states that a non-negative function belongs to the Hardy space H 1 (T) if and only if it belongs to L log L(T). We consider Bergman spaces of holomorphic functions in the upper half plane and develop avatars of Stein's Theorem and relative results in this context. We are led to consider weighted Bergman spaces and Bergman spaces of Musielak-Orlicz type. Eventually, we characterize bounded Hankel operators on A 1 (C +). This paper is dedicated to Eleonor Harboure, Pola, a colleague and friend whose memory will live on.

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hal-03883901 , version 1 (18-06-2025)

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  • HAL Id : hal-03883901 , version 1

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Aline Bonami, Sandrine Grellier, Benoit Sehba. Avatars of Stein's theorem in the complex setting. 2025. ⟨hal-03883901⟩
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