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arXiv · 2209.03510

Linear isometric invariants of bounded domains

Fusheng Deng·Jiafu Ning·Zhiwei Wang·Xiangyu Zhou
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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 $D$.

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Fusheng Deng, Jiafu Ning, Zhiwei Wang, Xiangyu Zhou. 2022-09-08. Linear isometric invariants of bounded domains. https://arxiv.org/abs/2209.03510

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