多圆柱上Bloch型空间之间加权复合算子的本性范数

设φ(z)=(φ1(z),…,φ_n(z))是D~n到自身的一个全纯映射,ψ(z)是D~n上的全纯函数,其中D~n是C~n中的单位多圆柱.研究了单位多圆柱上Bloch型空阊之间的加权复合算子ψC_φ的本性范数,并给出了其上下界估计.

The Essential Norms of Weighted Composition Operators Between Bloch-type Spaces in the Polydisc

Let $\varphi(z)=(\varphi_{1}(z),\cdots ,\varphi_{n}(z))$ be a holomorphic self-map of $\mathbb{D}^{n}$ and $\psi(z)$ a holomorphic function on $\mathbb{D}^{n}$, where $\mathbb{D}^{n}$ is the unit polydisc of $\mathbb{C}^{n}$. The authors investigate the essential norms of the weighted composition operator $\psi C_{\varphi}$ between Bloch-type spaces in the unit polydisc, and gives the lower and upper estimates of the essential norms.