فهرست نشریات علمی دسترسی آزاد ایران

Let $\mathbb{D}= \{\upsilon\in\mathbb{C}:|\upsilon|<1\}$ be the open unit disk in the complex plane $\mathbb{C}$ and let $H(\mathbb{D})$ be the space of all holomorphic functions on  $\mathbb{D}$. For a non-negative integer $n$ and a function $f \in H(\mathbb{D})$, the $n^{th}-$ order differentiation operator is defined as $D^n f = f^{(n)}$. The weighted composition operator together with $n^{th}-$ order differentiation operator give rise to a new operator generally termed as generalized weighted composition operator denoted by $\mathcal{W}^{n}_{\phi,\xi}$ and is  defined by\begin{equation*}\mathcal{W}^{n}_{\phi,\xi}f(\upsilon)  =\phi(\upsilon)f^{(n)}(\xi(\upsilon)),\quad f\in H(\mathbb{D}); \upsilon\in%\mathbb{D},\end{equation*}where $\phi\in H(\mathbb{D})$ and $\xi$ is a holomorphic self-map of $\mathbb{D}$. This operator is basically the combination of multiplication operator $M_{\phi}$, composition operator  $C_{\xi}$ and $n^{th}-$ order differentiation operator $D^{n}$. We study the boundedness and compactness of this operator between Dirichlet-type spaces and Bloch-type spaces.