On weighted Bergman spaces of a domain with Levi-flat boundary
On weighted Bergman spaces of a domain with Levi-flat boundary
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具有列维平坦边界的域的加权伯格曼空间
DOI：
10.1090/tran/8471
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
M. Adachi
中科院分区：
文献类型：
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作者：
Kamiya Ryo;Kanki Masataka;Mase Takafumi;Okubo Naoto;Tokihiro Tetsuji;Homare TADANO;Ryuichi Sato;神本晋吾;蛭子 彰仁;反田美香;Yu Ito;佐藤龍一;只野 誉;M. Adachi
本研究的目的是了解一个1-凸域的列维平坦边界在何种程度上能够全纯函数的缓慢增长。本文讨论了这类区域的一个典型例子：双曲紧致黎曼曲面上的所有测地线段空间。我们的主要发现是一个积分公式，产生全纯函数域上的全纯微分黎曼曲面。这种构造可以看作是具有最优常数的全纯函数的jet扩张的一个非平凡例子。作为其推论，证明了该域的加权Bergman空间对于任何大于的权阶都是无穷维的，尽管该域不允许任何非常数有界全纯函数.引用
The aim of this study is to understand to what extent a 1-convex domain with Levi-flat boundary is capable of holomorphic functions with slow growth. This paper discusses a typical example of such domain, the space of all the geodesic segments on a hyperbolic compact Riemann surface. Our main finding is an integral formula that produces holomorphic functions on the domain from holomorphic differentials on the Riemann surface. This construction can be seen as a non-trivial example ofjet extension of holomorphic functions with optimal constant. As its corollary, it is shown that the weighted Bergman spaces of the domain is infinite dimensional for any weight order greater thanin spite of the fact that the domain does not admit any non-constant bounded holomorphic functions. References