Essential Norms of Weighted Composition Operators between Hardy Spaces in the unit Ball

Details Essential Norms of Weighted Composition Operators between Hardy Spaces in the unit Ball Essential Norms of Weighted Composition Operators between Hardy Spaces in the unit Ball

2007-09-10

arxiv.org/abs/0709.1431v1

Mathematics

Functional Analysis

17 pages

Scientific paper

Let $\phi(z)=(\phi_1(z),...,\phi_n(z))$ be a holomorphic self-map of $B_n$ and $\psi(z)$ a holomorphic function on $B_n$, and $H(B_n)$ the class of all holomorphic functions on $B_n$, where $B_n$ is the unit ball of $C^n$, the weight composition operator $W_{\psi,\phi}$ is defined by $W_{\psi,\phi}=\psi f(\phi)$ for $f\in H(B_n)$. In this paper we estimate the essential norm for the weighted composition operator $W_{\psi,\phi}$ acting from the Hardy space $H^p$ to $H^q$ ($0

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