Bloch空间及其乘子代数的随机化

本项目致力于研究解析函数空间上的随机系数乘子。特别地，申请人将重点研究Bloch空间上的随机系数乘子。所谓随机系数乘子就是解析函数Taylor系数的随机化。申请人将从随机Taylor级数和系数乘子两个方面展开研究。主要考虑在三种对称分布（Rademacher分布、Steinhaus分布和Gaussian分布）下，对Bloch空间以及Bloch空间的乘子代数，研究随机系数乘子的初始空间中元素的刻画。然后，将从泛函分析的观点研究这两类空间上的度量结构及相应的函数性质。本项目将立足算子理论，进一步促进随机分析方法在算子理论中的应用。

This project is dedicated to the study of random coefficient multipliers on analytic function spaces. In particular, the applicant will focus on the random coefficient multipliers on the Bloch space. The so-called random coefficient multipliers are the randomization of the Taylor coefficient of analytic functions. The applicant will start from two aspects: random Taylor series and coefficient multipliers. Considering three symmetrical distributions (Rademacher distribution, Steinhaus distribution and Gaussian distribution), the applicant will seek to characterize the elements of the initial space of random coefficient multipliers for the Bloch space and its multiplier algebra. Then, from the perspective of functional analysis, the metric structure and the corresponding function properties on these two types of spaces will be studied. This project will be based on operator theory and further promote the application of stochastic analysis methods in operator theory.