对数Bloch空间上的乘子和循环元  

Multipliers and cyclic vectors in α-logarithmic Bloch spaces

作　　者：周智慧 叶善力[1] ZHOU Zhi-hui;Ye Shan-li(School of Sci.,Zhejiang Univ.of Sci.and Tech.,Hangzhou 310023,China)

机构地区：[1]浙江科技学院理学院,浙江杭州310023

出　　处：《高校应用数学学报（A辑）》2023年第4期483-490,共8页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11671357,11801508)。

摘　　要：对α∈R,定义α-对数Bloch空间为BL^(α)={f∈H(D):‖f‖L^(α)=sup_(z∈D)(1-|z|^(2))(loge/1-|z|^(2))^(α)|f’(z)|<∞}.该文研究了α-对数Bloch空间上的点乘子和循环元,给出了当α,β≠1时,点乘空间M(BL^(α),BL^(β))的刻划,也给出了α-对数Bloch空间上循环元的一些性质.特别地,当α>1时,f是BL^(α)的循环元当且仅当f在闭单位圆盘上没有零点.Suppose a E R.Define α-logarithmic Bloch space to be BL^(α)={||f||L^(α)=sup_(z∈H)(1-|z|^(2))(loge/1-|z|^(2))^(α)|f'(z)|<∞}.In this paper,the pointwise multipliers and cyclic vectors in the a-logarithmic Bloch space are firstly studied.Secondly,the characterizations of the pointwise multiplier space M(BL^(α),BL^(β))are given,and also some properties of cyclic vectors in the α-logarithmic Bloch space are obtained.In particular,for α>1,it is obtained that f is cyclic in BL^(α) if and only if f has no zeros in the closed unit disc.

关 键 词：点乘子 循环元 α-对数Bloch空间 

分 类 号：O174.5[理学—数学]