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The Carleson Measure Problem Between Analytic Morrey Spaces

Published online by Cambridge University Press:  20 November 2018

Jianfei Wang
Jianfei Wang*
Affiliation:
Mathematics, Physics and Information Engineering, ZhejiangNormalUniversity, Jinhua, Zhejiang, 321004, China e-mail: wangjf@mail.ustc.edu.cn
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Abstract

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The purpose of this paper is to characterize positive measure $\mu$ on the unit disk such that the analytic Morrey space $\mathcal{A}{{\mathcal{L}}_{p,\eta }}$ is boundedly and compactly embedded to the tent space

$$\mathcal{J}_{q,1-\frac{q}{p}\left( 1-\eta \right)}^{\infty }\left( \mu \right)$$

for the case $1\,\le \,q\,\le \,p\,<\,\infty$ respectively. As an application, these results are used to establish the boundedness and compactness of integral operators and multipliers between analytic Morrey spaces.

Keywords

30H3528A1247B3846E15Morrey spaceCarleson measure problemboundednesscompactness
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 59 , Issue 4 , 01 December 2016 , pp. 878 - 890
Copyright
Copyright © Canadian Mathematical Society 2016

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