On Weighted Banach Spaces of Vector- Valued Holomorphic Functions

Document Type : Original Article

Authors

Department of Mathematics, Bu-Ali Sina University, Hamedan, Iran

Abstract

‎Let $X$ be a complex Banach space, $\mathbb{D}$ the unit disc, and $\upsilon$ a weight function. We investigate the weighted spaces of vector-valued holomorphic functions $H_{\upsilon}(\mathbb{D}, X)$. In particular, we study the boundedness and compactness of differentiation and composition operators on these spaces. Additionally, we examine the relationships among the algebraic structure of $H_{\upsilon}(\mathbb{D}, \mathcal{A})$, the Banach algebra $\mathcal{A}$, and the weight function $\upsilon$.

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References

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