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.
Rezaei, S., & Hassanlou, M. (2020). Composition operators between growth spaces on circular and strictly convex domains in complex Banach spaces. Caspian Journal of Mathematical Sciences, 9(2), 182-190. doi: 10.22080/cjms.2020.15630.1370
MLA
shayesteh Rezaei; Mostafa Hassanlou. "Composition operators between growth spaces on circular and strictly convex domains in complex Banach spaces". Caspian Journal of Mathematical Sciences, 9, 2, 2020, 182-190. doi: 10.22080/cjms.2020.15630.1370
HARVARD
Rezaei, S., Hassanlou, M. (2020). 'Composition operators between growth spaces on circular and strictly convex domains in complex Banach spaces', Caspian Journal of Mathematical Sciences, 9(2), pp. 182-190. doi: 10.22080/cjms.2020.15630.1370
VANCOUVER
Rezaei, S., Hassanlou, M. Composition operators between growth spaces on circular and strictly convex domains in complex Banach spaces. Caspian Journal of Mathematical Sciences, 2020; 9(2): 182-190. doi: 10.22080/cjms.2020.15630.1370
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