This project aims to use the theories and methods of modern complex analysis and harmonic analysis to study the basic theories of several important types of analytic function spaces and related operator theories in the field of complex analysis, explore new methods, solve basic problems, and establish and improve the general theory of analytic function spaces.
The project mainly studies two important types of analytic function spaces: Fock type spaces and Q-type spaces. These two types of function spaces are important in complex analysis, harmonic analysis, and functional analysis, and are closely related to quantum mechanics and differential equations. The main contents of the project research include: studying Fock type spaces, their operators and related application problems, establishing the basic theory of high-dimensional Q-type spaces, studying multiplication operators on analytic function spaces, studying weak products of function spaces, and studying the topological structure of bounded composite operator spaces on analytic function spaces.