小Bloch空间和Besov空间上加权复合算子的超循环性

Hypercyclicity of weighted composition operators on the Little Bloch Space and the Besov space

摘要:

文章主要描述了小Bloch空间和Besov空间上加权复合算子的超循环性.证明了解析自映射是自同构时,加权复合算子(权为复数时)在小Bloch空间和Besov空间上都不是超循环的,同时给出解析自映射是非自同构时,权在一定条件下,加权复合算子在小Bloch空间和Besov空间上的超循环性.

Abstract:

We characterize the hypercyclicity of weighted composition operators on the Little Bloch Space and the Besov space.We obtain that there are no hypercyclic composition operators on the Little Bloch Space and the Besov space when holomorphic self-map is an automorphism.And when holomorphic self-map is a non-automorphism,we discuss the hypercyclicity of weighted composition operators on the Little Bloch Space and the Besov space under certain conditions.