Analysis of Cesaro-type integral operators via function-theoretic properties of symbol functions

本文研究了单位圆盘或单位球上的全纯函数所构成的Bergman空间以及作用在这些空间上的积分型算子、复合算子和加权复合算子。我们的目的是通过符号函数和自映射的函数论性质来刻画这些算子的算子论性质。进而利用Berezin型变换估计了这类算子的算子范数和本质范数，并引入了由全纯函数构成的Zygmund F-代数。这个函数空间包含所有的Bergman空间和Nevanlinna型空间。研究了Zygmund F-代数上的线性等距或乘法等距的结构。

In this research, we considered the Bergman spaces which consist of holomorphic functions on the unit disk or the unit ball and integral type operators, composition operators and weighted composition operators acting on these spaces. Our purposes are to characterize operator-theoretic properties of these operators via function-theoretic properties of symbol functions and self-maps. Furthermore we will estimate the operator norm and the essential norm for these type operators by Berezin-type transforms.Also we introduced the Zygmund F-algebra which consists of holomorphic functions. This function space contains all Bergman spaces and Nevanlinna type spaces. We investigated the structure of linear isometries or multiplicative isometries on the Zygmund F-algebra.