Weighted Differentiation Composition Operators from Weighted Bergman Spaces with Admissible Weights to Bloch-type Spaces
Subject Areas : International Journal of Industrial Mathematics
شایسته رضایی
1
(
Department of Mathematics, Aligudarz Branch, Islamic Azad University, Aligudarz, Iran.
)
Keywords: Bloch-type space, Compactness, Boundedness, Weighted Bergman space, Admissible weight, Weighted differentiation composition operator,
Abstract :
For an analytic self-map $\varphi$ of the unit disk $\mathbb{D}$ in the complex plane $\mathbb{C}$, a nonnegative integer $n$, and $u$ analytic function on $\mathbb{D}$, weighted differentiation composition operator is defined by $(D_{\varphi,u}^nf) (z)=u(z)f^{(n)}(\varphi(z))$, where $f$ is an analytic function on $\mathbb{D}$ and $z\in\mathbb{D}$. In this paper, we study the boundedness and compactness of $D_{\varphi,u}^n$, from weighted Bergman spaces with admissible weights to Bloch-type spaces.
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