Geodesic
Linear isometric invariants of bounded domains
Izvestiya. Mathematics , Tome 88 (2024) no. 4, pp. 626-638

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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 $D$.
Keywords: linear isometry, $A^p$-complete, biholomorphic equivalent. 
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     title = {Linear isometric invariants of bounded domains},
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Fusheng Deng; Jiafu Ning; Zhiwei Wang; Xiangyu Zhou. Linear isometric invariants of bounded domains. Izvestiya. Mathematics , Tome 88 (2024) no. 4, pp. 626-638. http://geodesic.mathdoc.fr/item/IM2_2024_88_4_a1/