对数Bloch型空间上微分复合算子乘积的本性范数

Product of Differentiation and Composition Operators on theLogarithmic Bloch Type Space

目的为刻画微分复合算子乘积C_(φ)D^(m)在对数Bloch型空间上的本性范数特征。方法利用有界序列{z^(n)}∞n=1刻画对数Bloch型空间上微分复合算子乘积C_(φ)D^(m)的有界性特征,以及泛函分析中的算子理论,例如紧算子性质和对本性范数上下界的估计。结果在C_(φ)D^(m)有界的条件下,给出了微分复合算子C_(φ)D^(m)的本性范数特征,即这里m为非负正整数,微分复合算子乘积为C_(φ)D^(m)f=f(m)°φ。结论在C_(φ)D^(m)有界的条件下,则微分复合算子C_(φ)D^(m)的本性范数可由有界序列{z^(n)}∞n=1的特征刻画。

Objective To characterize the boundedness and essential norms of the product of differentiation and composition operators C_(φ)D^(m)on logarithmic Bloch type spaces.Methods A bounded sequence{z^(n)}∞n=1 was used to characterize the boundedness of the product of differential composite operators C_(φ)D^(m)on logarithmic Bloch type spaces and the operator theory in functional analysis,such as the properties of compact operators.Results The essential norm of the product of differentiation and composition operators C_(φ)D^(m)on the logarithmic Bloch type was obtained.Here m is a nonnegative positive integer,and the product of the differentiation and composition operator C_(φ)D^(m)is defined by C_(φ)D^(m)f=f(m)°φ.Conclusion If the product of differential composite operators C_(φ)D^(m)on logarithmic Bloch type spaces is bounded,the essential norm of C_(φ)D^(m)may be characterized by the characteristics of the bounded sequence{z^(n)}.