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Analytic Besov spaces, approximation, and closed ideals

Part of: Spaces and algebras of analytic functions

Published online by Cambridge University Press:  13 May 2022

Hafid Bahajji-El Idrissi  and
Hamza El Azhar Open the ORCID record for Hamza El Azhar [Opens in a new window]
Hafid Bahajji-El Idrissi*
Affiliation:
Laboratory of Mathematical Analysis and Applications, École Normale Supérieure de Rabat, Mohammed V University in Rabat, B.O. 5118, 10105 Rabat, Morocco
Hamza El Azhar
Affiliation:
Faculty of sciences, Chouaib Doukkali University, B.O. 24000, El Jadida, Morocco e-mail: elazharhamza@gmail.com
*
e-mail: bahajjielidrissihafid@gmail.com
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Abstract

In this paper, we give a complete description of closed ideals of the Banach algebra $\mathcal {B}^{s}_{p}\cap \lambda _{\alpha }$ , where $\mathcal {B}^{s}_{p}$ denotes the analytic Besov space and $\lambda _{\alpha }$ is the separable analytic Lipschitz space. Our result extends several previous results in Bahajji-El Idrissi and El-Fallah (2020, Studia Mathematica 255, 209–217), Bouya (2009, Canadian Journal of Mathematics 61, 282–298), and Shirokov (1982, Izv. Ross. Akad. Nauk Ser. Mat. 46, 1316–1332).

Keywords

Besov spacesLipschitz algebrasclosed ideals

MSC classification

Primary: 30H25: Besov spaces and $Q_p$-spaces
Secondary: 30H50: Algebras of analytic functions
Type
Article
Information
Canadian Mathematical Bulletin , Volume 66 , Issue 1 , March 2023 , pp. 259 - 268
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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Footnotes

In memory of the late Brahim Bouya (1977–2020)

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