Composition operators between growth spaces on circular and strictly convex domains in complex Banach spaces
Publish place: Caspian Journal of Mathematical Sciences، Vol: 9، Issue: 2
Publish Year: 1399
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_CJMS-9-2_003
تاریخ نمایه سازی: 27 بهمن 1399
Abstract:
Let $\Omega_X$ be a bounded, circular and strictly convex domain in a complex Banach space $X$, and $\mathcal{H}(\Omega_X)$ be the space of all holomorphic functions from $\Omega_X$ to $\mathbb{C}$. The growth space $\mathcal{A}^\nu(\Omega_X)$ consists of all $f\in\mathcal{H}(\Omega_X)$ such that $|f(x)|\leqslant C \nu(r_{\Omega_X}(x)),\quad x\in \Omega_X,$ for some constant $C>0$, whenever $r_{\Omega_X}$ is the Minkowski functional on $\Omega_X$ and $\nu :[0,1)\rightarrow(0,\infty)$ is a nondecreasing, continuous and unbounded function. For complex Banach spaces $X$ and $Y$ and a holomorphic map $\varphi:\Omega_X\rightarrow\Omega_Y$, put $C_\varphi( f)=f\circ \varphi,f\in\mathcal{H}(\Omega_Y)$. We characterize those $\varphi$ for which the composition operator $ C_\varphi:\mathcal{A}^{\omega}(\Omega_Y)\rightarrow\mathcal{A}^{\nu}(\Omega_X)$ is a bounded or compact operator.
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