Annals of Functional Analysis

Embedding theorems and integration operators on Bergman spaces with exponential weights

Xiaofen Lv

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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<.

Article information

Source
Ann. Funct. Anal., Volume 10, Number 1 (2019), 122-134.

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

Permanent link to this document
https://projecteuclid.org/euclid.afa/1547629228

Digital Object Identifier
doi:10.1215/20088752-2018-0013

Mathematical Reviews number (MathSciNet)
MR3899961

Zentralblatt MATH identifier
07045490

Subjects
Primary: 30H20: Bergman spaces, Fock spaces
Secondary: 47B34: Kernel operators

Keywords
Bergman spaces with exponential weights Carleson measures boundedness compactness

Citation

Lv, Xiaofen. Embedding theorems and integration operators on Bergman spaces with exponential weights. Ann. Funct. Anal. 10 (2019), no. 1, 122--134. doi:10.1215/20088752-2018-0013. https://projecteuclid.org/euclid.afa/1547629228


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