Linear isometric invariants of bounded domains
- Authors: Deng F.1, Ning J.2, Wang Z.3, Zhou X.4,5,1
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Affiliations:
- School of Mathematical Sciences, University of the Chinese Academy of Sciences
- Central South University, Changsha
- Beijing Normal University
- Academy of Mathematics and Systems Science, Chinese Academy of Sciences
- Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences
- Issue: Vol 88, No 4 (2024)
- Pages: 31-43
- Section: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/261163
- DOI: https://doi.org/10.4213/im9542
- ID: 261163
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Abstract
We introduce two new conditions for bounded domains, namely $A^p$-completeness and boundary blow down type, and show that, for two bounded domains $D_1$ and $D_2$ that are $A^p$-complete and not of boundary blow down type, if there exists a linear isometry from $A^p(D_1)$ to $A^{p}(D_2)$ for some real number $p>0$ with $p\neq $ even integers, then $D_1$ and $D_2$ must be holomorphically equivalent, where, for a domain $D$, $A^p(D)$ denotes the space of $L^p$ holomorphic functions on $D$.Bibliography: 13 titles.
About the authors
Fusheng Deng
School of Mathematical Sciences, University of the Chinese Academy of Sciences
Jiafu Ning
Central South University, Changsha
Zhiwei Wang
Beijing Normal University
Xiangyu Zhou
Academy of Mathematics and Systems Science, Chinese Academy of Sciences; Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences; School of Mathematical Sciences, University of the Chinese Academy of Sciences
Email: xyzhou@math.ac.cn
PhD
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