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Compact and order bounded sum of weighted differentiation composition operators
- Publication Year :
- 2022
-
Abstract
- In this paper, we characterize bounded, compact and order bounded sum of weighted differentiation composition operators from Bergman type spaces to weighted Banach spaces of analytic functions, where the sum of weighted differentiation composition operators is defined as $$ S^{n}_{\vec{u},\tau}(f)= \displaystyle\sum_{j=0}^{n}D_{u_{j} ,\tau}^{j}(f), \; \; f \in \mathcal{H}(\mathbb D).$$ Here $\mathcal{H}(\mathbb D)$ is the space of all holomorphic functions on $\mathbb D$, $\vec{u}=\{u_{j}\}_{j=0}^{n}$, $u_{j} \in \mathcal{H}(\mathbb{D})$, $\tau$ a holomorphic self-map of $\mathbb D$, $f^{(j)}$ the $j$th derivative of $f$ and weighted differentiation composition operator $D_{u_{j},\tau}^{j}$ is defined as $D_{u_{j},\tau}^{j}(f)=u_{j}C_{\tau}D^{j}(f)=u_{j}f^{(j)}\circ\tau, \; \; f \in \mathcal{H}(\mathbb D).$
- Subjects :
- Mathematics - Functional Analysis
Primary 47B38, 47A55, Secondary 30D55
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2211.08845
- Document Type :
- Working Paper