A note on the Berezin transform on the generalized Hartogs triangles

Zou, Qingyang

doi:10.1007/s00013-024-01971-5

Arch. Math.

2024

DOI: 10.1007/s00013-024-01971-5

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A note on the Berezin transform on the generalized Hartogs triangles

Qingyang Zou

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2024

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Cited by 2 publications

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Regularity of the Berezin Transform on the Elementary Reinhardt Domains

Yang,

Zou

2024

Complex Anal. Oper. Theory

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Regularity of the Berezin Transform on the Elementary Reinhardt Domains

Yang,

Zou

2024

Complex Anal. Oper. Theory

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$L^p$ -BOUNDEDNESS OF THE BEREZIN TRANSFORM ON GENERALISED HARTOGS TRIANGLES

ZOU

2024

Bull. Aust. Math. Soc.

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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 $p>nk+1$ .

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A note on the Berezin transform on the generalized Hartogs triangles

Cited by 2 publications

References 18 publications

Regularity of the Berezin Transform on the Elementary Reinhardt Domains

Regularity of the Berezin Transform on the Elementary Reinhardt Domains

$L^p$ -BOUNDEDNESS OF THE BEREZIN TRANSFORM ON GENERALISED HARTOGS TRIANGLES

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