Avatars of Stein's theorem in the complex setting

Authors

  • Aline Bonami Institut Denis Poisson, Département de Mathématiques, Université d'Orléans, 45067 Orl´eans Cedex 2, France
  • Sandrine Grellier Institut Denis Poisson, Département de Mathématiques, Université d’Orléans, 45067 Orl´eans Cedex 2, France
  • Benoît Sehba Department of Mathematics, University of Ghana, P.O. Box LG 62 Legon, Accra, Ghana

DOI:

https://doi.org/10.33044/revuma.4361

Abstract

In this paper, we establish some variants of Stein's theorem, which states that a non-negative function belongs to the Hardy space $H^1(\mathbb{T})$ if and only if it belongs to $L\log L(\mathbb{T})$. 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 $A^1(\mathbb{C}_+)$.

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References

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Photo of Eleonor Harboure, courtesy of Marcela Porta

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Published

2023-09-21

Issue

Vol. 66 No. 1 (2023): Special volume in honour of Eleonor Harboure (1948–2022)

Section

Article

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Copyright (c) 2023 Aline Bonami, Sandrine Grellier, Benoît Sehba

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