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.
Cesàro operator unit ball Bloch spaces boundedness compactness
The Science and Technology Planning Project of Quang Ngai Province
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Matematik |
Yazarlar | |
Erken Görünüm Tarihi | 10 Ocak 2024 |
Yayımlanma Tarihi | 27 Ağustos 2024 |
Yayımlandığı Sayı | Yıl 2024 Cilt: 53 Sayı: 4 |