On the boundedness and compactness of extended Cesàro composition operators between weighted Bloch-type spaces

Year 2024, Volume: 53 Issue: 4, 894 - 914, 27.08.2024

Lien Vuong Lam , Thai Thuan Quang

https://doi.org/10.15672/hujms.1197627

Abstract

Let $\psi \in H(\mathbb{B}_n),$ the space of all holomorphic functions on the unit ball $\mathbb{B}_n$ of $\mathbb{C}^n,$ $\varphi = (\varphi_1, \ldots, \varphi_n) \in S(\mathbb{B}_n)$ the set of holomorphic self-maps of $\mathbb{B}_n.$ Let $C_{\psi, \varphi}: \mathcal B_{\nu}$ (and $ \mathcal B_{\nu,0}$) $\to \mathcal B_{\mu} $ (and $ \mathcal B_{\mu,0}$) be weighted extended Cesàro operators induced by products of the extended Cesàro operator $ C_\varphi $ and integral operator $T_\psi.$ In this paper, we characterize the boundedness and compactness of $ C_{\psi,\varphi} $ via the estimates for either $ |\varphi| $ or $ |\varphi_k| $ for some $ k\in \{1,\ldots,n\}. $ At the same time, we also give the asymptotic estimates of the norms of these operators.

Keywords

Cesàro operator, unit ball, Bloch spaces, boundedness, compactness

Supporting Institution

The Science and Technology Planning Project of Quang Ngai Province

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