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Corona and Wolff theorems for the multiplier algebra of Dirichlet–Morrey spaces

Part of: Spaces and algebras of analytic functions

Published online by Cambridge University Press:  13 January 2022

Lian Hu ,
Songxiao Li Open the ORCID record for Songxiao Li [Opens in a new window]  and
Rong Yang
Lian Hu
Affiliation:
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, 610054 Sichuan, P.R. China e-mail: 201921210220@std.uestc.edu.cn 201921210221@std.uestc.edu.cn
Songxiao Li*
Affiliation:
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, 610054 Sichuan, P.R. China e-mail: 201921210220@std.uestc.edu.cn 201921210221@std.uestc.edu.cn
Rong Yang
Affiliation:
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, 610054 Sichuan, P.R. China e-mail: 201921210220@std.uestc.edu.cn 201921210221@std.uestc.edu.cn
*
e-mail: lisongxiao@uestc.edu.cn
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Abstract

For $0<\lambda ,p<1$ , the Dirichlet–Morrey space $\mathcal {D}_p^{\lambda } $ is the space of all analytic function on the unit disc such that the measure $ |f'(z)|^2(1-|z|^2)^pdA(z)$ is a $p\lambda $ -Carleson measure. In this paper, we show that the corona theorem and the Wolff theorem hold for the multiplier algebra of Dirichlet–Morrey spaces.

Keywords

Dirichlet–Morrey spacecorona theoremWolff theoremCarleson measure

MSC classification

Primary: 30H80: Corona theorems
Secondary: 30H99: None of the above, but in this section
Type
Article
Information
Canadian Mathematical Bulletin , Volume 65 , Issue 4 , December 2022 , pp. 963 - 975
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Copyright
© Canadian Mathematical Society, 2022

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