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Embedding Theorems for Dirichlet Type Spaces

Part of: Special classes of linear operators Spaces and algebras of analytic functions

Published online by Cambridge University Press:  22 July 2019

Songxiao Li ,
Junming Liu  and
Cheng Yuan
Songxiao Li
Affiliation:
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, 610054, Chengdu, Sichuan, P. R. China Email: jyulsx@163.com
Junming Liu
Affiliation:
School of Applied Mathematics, Guangdong University of Technology, Guangzhou, Guangdong510006, P. R. China Email: jmliu@gdut.edu.cnyuancheng1984@163.com
Cheng Yuan
Affiliation:
School of Applied Mathematics, Guangdong University of Technology, Guangzhou, Guangdong510006, P. R. China Email: jmliu@gdut.edu.cnyuancheng1984@163.com
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Abstract

We use the Carleson measure-embedding theorem for weighted Bergman spaces to characterize the positive Borel measures $\unicode[STIX]{x1D707}$ on the unit disc such that certain analytic function spaces of Dirichlet type are embedded (compactly embedded) in certain tent spaces associated with a measure $\unicode[STIX]{x1D707}$. We apply these results to study Volterra operators and multipliers acting on the mentioned spaces of Dirichlet type.

Keywords

Dirichlet type spaceCarleson measureVolterra integral operator

MSC classification

Primary: 30H99: None of the above, but in this section
Secondary: 47B38: Operators on function spaces (general)
Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 1 , March 2020 , pp. 106 - 117
Copyright
© Canadian Mathematical Society 2019

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Footnotes

J. Liu is the corresponding author. This work was supported by NNSF of China (Grant No. 11801094 and No.11720101003).

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