Abstract
In this paper, we consider a class of logarithmically convex domains in \({\mathbb {C}}^n\), called elementary Reinhardt domains, which can be regarded as a natural generalization of Hartogs triangles. The purpose of this paper is twofold. On one hand, we will compute the explicit forms of the Bergman kernel of weighted Hilbert space with radial symbols. On the other hand, by using the expressions of the weighted Bergman kernel, we will show the regularity of the Berezin transform on the elementary Reinhardt domains.
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Acknowledgements
We sincerely thank the referees, who read the paper carefully and gave many useful suggestions which improve the presentation of the manuscript greatly. This work was partly supported by the National Natural Science Foundation of China (No.11901327). Zou was supported by the Science and Technology Research Project of Hubei Provincial Department of Education Q20191109.
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LY and QZ wrote the main manuscript text together. All the authors reviewed the manuscript.
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Communicated by Aurelian Gheondea.
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Yang, L., Zou, Q. Regularity of the Berezin Transform on the Elementary Reinhardt Domains. Complex Anal. Oper. Theory 18, 97 (2024). https://doi.org/10.1007/s11785-024-01538-w
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DOI: https://doi.org/10.1007/s11785-024-01538-w