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Article contents
$L^p$-BOUNDEDNESS OF THE BEREZIN TRANSFORM ON GENERALISED HARTOGS TRIANGLES
Part of:
Special classes of linear operators
Holomorphic functions of several complex variables
Integral, integro-differential, and pseudodifferential operators
Published online by Cambridge University Press: 04 October 2024
Abstract
We study the 
$L^p$-boundedness of the Berezin transform on the generalised Hartogs triangles which are defined by 
$$ \begin{align*}H_k:=\{(z, w)\in\mathbb C^n\times\mathbb C: |z_1|^2+\cdots+|z_n|^2<|w|^{2k}<1\},\end{align*} $$
where 
$z=(z_1, \ldots , z_n)$ and 
$k\in \mathbb N$. We prove that the Berezin transform is bounded on 
$L^p(H_k)$ if and only if 
$p>nk+1$.
Keywords
MSC classification
Primary:
32A36: Bergman spaces
- Type
- Research Article
- Information
- Copyright
- © The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.
Footnotes
This work is supported by the Science and Technology Research Project of Hubei Provincial Department of Education, Grant No. Q20191109.
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