Weighted Composition Operators between different Bloch-type Spaces in Polydisk

Details Weighted Composition Operators between different Bloch-type Spaces in Polydisk Weighted Composition Operators between different Bloch-type Spaces in Polydisk

2005-03-27

arxiv.org/abs/math/0503622v2

Mathematics

Complex Variables

27 Pages

Scientific paper

Let $\phi(z)=(\phi_1(z), ...,\phi_n(z))$ be a holomorphic self-map of $U^n$ and $\psi(z)$ a holomorphic function on $U^n,$ where $U^n$ is the unit polydisk of ${\Bbb C}^n.$ Let $p\geq 0,$ $q\geq 0$, this paper gives some necessary and sufficient conditions for the weighted composition operator $W_{\psi,\phi}$ induced by $\psi$ and $\phi$ to be bounded and compact between $p$-Bloch space ${\cal B}^p(U^n)$ and $q$-Bloch space ${\cal B}^q(U^n).$

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