Weighted Differentiation Composition Operators from Weighted Bergman Spaces with Admissible Weights to Bloch-type Spaces

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.

Keywords:

Weighted differentiation composition operator , Weighted Bergman space , Bloch-type space , Admissible weight , Boundedness , ‎ ‎Compactness