从B_(log)~α空间到Q_k空间的复合算子

Composition Operators from B_(log)~α Spaces to Q_K

算子理论是函数空间理论研究的一个重要分支,函数空间上复合算子的有界性、紧性的研究与函数空间自身的函数性质密不可分;虽然不同的解析函数空间有着许多相似的函数理论,但其上的复合算子的有界性、紧性、K-Carleson测度的刻画往往取决于每个函数空间的特殊性及算子本身的性质.把算子与函数空间放在一起讨论是深入研究算子、函数空间的佳径,近年来国内外的研究动态就是很好的证明.Blαog空间是经典Bloch空间的子空间,而Bloch型空间和QK空间一直都是研究的热点;主要利用复分析、泛函分析的理论与方法讨论了Blαog空间到QK空间的复合算子,利用K-Carleson测度刻画了Blαog空间到QK空间的复合算子,得到了该算子为有界和紧的充要条件;此结果是Bloch型空间到QK空间上复合算子为有界和紧的一种全新的刻画.

Operator theory is an important branch in the theory of function spaces. The study of boundedness, compactness of composition operator is closely related to the properties of functions in the space. Even though there is a lot of similar function theory in different function space, the boundedness, compacledness and K-Carleson measure of composition operator more depend on the special properties of function spaces and the operator itseff. From the development of this field in recently years all over the world, it shows that take the operator theory and function spaces theory is a good way to study deeply operator theory and functions spaces. B^αlog space is a subspace of classical Bloch space, and the study of Bloch-type space and Qk space is also attract a lot of mathematicians. In this paper, we discuss the composition operator from B^αlog spaces to Qk spaces, the main tools are the theory of complex analysis and functional analysis. We characterize the composition operator from B^αlog spaces to Qk. spaces.with K-Carleson measure and get a sufficient and necessary condition of the boundedness and compactness. This result gives a new characterization of the boundedness and compactness of composition operator from Bloeh-type space to Qk spaces.