对数Bloch空间上的乘子和循环元

Multipliers and cyclic vectors in α-logarithmic Bloch spaces

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.