对数Bloch类空间与n阶加权类空间之间的加权微分复合算子

Weighted differentiation composition operators between logarithmic Bloch type spaces and nth weighted type spaces

本文研究了从对数Bloch类空间B_(logβ)^(α)到n阶加权类空间W_(μ)^(n)的加权微分复合算子D_(φ,u)^(m)的有界性和紧性,同时当权函数μ(z)=να,β(z)时,也刻画了从n阶加权类空间W_(να,β)^((n))到对数Bloch类空间B_(logβ)^(α)的加权微分复合算子D_(φ,u)^(m)是有界和紧的充要条件。

This paper characterizes the boundedness and compactness of weighted differentiation composition operators D_(φ,u)^(m) from logarithmic Bloch type spaces B_(logβ)^(α) to nth weighted type spaces W(n)μ.When μ(z)=να,β(z),it is also showed that the necessary and sufficient conditions for the boundedness and compactness of the D_(φ,u)^(m) from W_(να,β)^((n)) to B_(logβ)^(α).