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Characterizations of Morrey type spaces

Part of: Special classes of linear operators Spaces and algebras of analytic functions Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  14 May 2021

Fangmei Sun  and
Hasi Wulan
Fangmei Sun
Affiliation:
Department of Mathematics, Shantou University, Shantou515063, People’s Republic of China e-mail: 18fmsun@stu.edu.cn
Hasi Wulan*
Affiliation:
Department of Mathematics, Shantou University, Shantou515063, People’s Republic of China e-mail: 18fmsun@stu.edu.cn
*
e-mail: wulan@stu.edu.cn
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Abstract

For a nondecreasing function $K: [0, \infty)\rightarrow [0, \infty)$ and $0<s<\infty $ , we introduce a Morrey type space of functions analytic in the unit disk $\mathbb {D}$ , denoted by $\mathcal {D}^s_K$ . Some characterizations of $\mathcal {D}^s_K$ are obtained in terms of K-Carleson measures. A relationship between two spaces $\mathcal {D}^{s_1}_K$ and $\mathcal {D}^{s_2}_K$ is given by fractional order derivatives. As an extension of some known results, for a positive Borel measure $\mu $ on $\mathbb {D}$ , we find sufficient or necessary condition for the embedding map $I: \mathcal {D}^{s}_{K}\mapsto \mathcal {T}^s_{K}(\mu)$ to be bounded.

Keywords

Morrey type spaceK-Carleson measureembedding mapfractional order derivative

MSC classification

Primary: 30H25: Besov spaces and $Q_p$-spaces
Secondary: 30D45: Bloch functions, normal functions, normal families 30D99: None of the above, but in this section 47B38: Operators on function spaces (general)
Type
Article
Information
Canadian Mathematical Bulletin , Volume 65 , Issue 2 , June 2022 , pp. 328 - 344
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Copyright
© Canadian Mathematical Society 2021

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Footnotes

This research is supported by the National Natural Science Foundation of China (Grant Number 11720101003)

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