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February 2019 Embedding theorems and integration operators on Bergman spaces with exponential weights
Xiaofen Lv
Ann. Funct. Anal. 10(1): 122-134 (February 2019). DOI: 10.1215/20088752-2018-0013

Abstract

In this article, given some positive Borel measure μ, we define two integration operators to be

Iμ(f)(z)=Df(w)K(z,w)e2φ(w)dμ(w) and

Jμ(f)(z)=D|f(w)K(z,w)|e2φ(w)dμ(w). We characterize the boundedness and compactness of these operators from the Bergman space Aφp to Lφq for 1<p,q<, where φ belongs to a large class W0, which covers those defined by Borichev, Dhuez, and Kellay in 2007. We also completely describe those μ’s such that the embedding operator is bounded or compact from Aφp to Lφq(dμ), 0<p,q<.

Citation

Download Citation

Xiaofen Lv. "Embedding theorems and integration operators on Bergman spaces with exponential weights." Ann. Funct. Anal. 10 (1) 122 - 134, February 2019. https://doi.org/10.1215/20088752-2018-0013

Information

Received: 15 March 2018; Accepted: 23 May 2018; Published: February 2019
First available in Project Euclid: 16 January 2019

zbMATH: 07045490
MathSciNet: MR3899961
Digital Object Identifier: 10.1215/20088752-2018-0013

Subjects:
Primary: 30H20
Secondary: 47B34

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.10 • No. 1 • February 2019
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