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

Authors : Lien Vuong Lam, Thai Thuan Quang

Pages : 894-914

Doi:10.15672/hujms.1197627

View : 323 | Download : 357

Publication Date : 2024-08-27

Article Type : Research Paper

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