论文标题
有限域的线性等距不变性
Linear isometric invariants of bounded domains
论文作者
论文摘要
我们介绍了有界域的两个新条件，即$ a^p $ completentes and Billow down类型，并表明，对于两个有界域$ d_1 $和$ d_2 $的$ a^p $ - complete而不是边界吹入类型，而不是$ a^p（$ a^p y $ p} $ p}（d_ p}（d_ p}（d_ p}） $ p \ neq $甚至整数，然后$ d_1 $和$ d_2 $必须是全态等效的，其中$ d $，$ a^p（d）$表示$ l^p $ holomorphic函数的空间$ d $。
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 $D$.
