Rezaei, S. (2015). Weighted composition operators between growth spaces on circular and strictly convex domain. Sahand Communications in Mathematical Analysis, 02(1), 51-56.

Shayesteh Rezaei. "Weighted composition operators between growth spaces on circular and strictly convex domain". Sahand Communications in Mathematical Analysis, 02, 1, 2015, 51-56.

Rezaei, S. (2015). 'Weighted composition operators between growth spaces on circular and strictly convex domain', Sahand Communications in Mathematical Analysis, 02(1), pp. 51-56.

Rezaei, S. Weighted composition operators between growth spaces on circular and strictly convex domain. Sahand Communications in Mathematical Analysis, 2015; 02(1): 51-56.

Weighted composition operators between growth spaces on circular and strictly convex domain

^{}Department of Pure Mathematics, Aligudarz Branch, Islamic Azad University, Aligudarz, Iran.

Abstract

Let $\Omega_X$ be a bounded, circular and strictly convex domain of a Banach space $X$ and $\mathcal{H}(\Omega_X)$ denote the space of all holomorphic functions defined on $\Omega_X$. The growth space $\mathcal{A}^\omega(\Omega_X)$ is the space of all $f\in\mathcal{H}(\Omega_X)$ for which $$|f(x)|\leqslant C \omega(r_{\Omega_X}(x)),\quad x\in \Omega_X,$$ for some constant $C>0$, whenever $r_{\Omega_X}$ is the Minkowski functional on $\Omega_X$ and $\omega :[0,1)\rightarrow(0,\infty)$ is a nondecreasing, continuous and unbounded function. Boundedness and compactness of weighted composition operators between growth spaces on circular and strictly convex domains were investigated.

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