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# The Carleson Measure Problem Between Analytic Morrey Spaces

Published:2016-03-23
Printed: Dec 2016
• Jianfei Wang,
Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, Zhejiang, 321004, China
 Format: LaTeX MathJax PDF

## Abstract

The purpose of this paper is to characterize positive measure $\mu$ on the unit disk such that the analytic Morrey space $\mathcal{AL}_{p,\eta}$ is boundedly and compactly embedded to the tent space $\mathcal{T}_{q,1-\frac{q}{p}(1-\eta)}^{\infty}(\mu)$ for the case $1\leq q\leq p\lt \infty$ respectively. As an application, these results are used to establish the boundedness and compactness of integral operators and multipliers between analytic Morrey spaces.
 Keywords: Morrey space, Carleson measure problem, boundedness, compactness
 MSC Classifications: 30H35 - BMO-spaces 28A12 - Contents, measures, outer measures, capacities 47B38 - Operators on function spaces (general) 46E15 - Banach spaces of continuous, differentiable or analytic functions

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