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Generalized weighted composition operators acting between Dirichlet-type spaces and Bloch-type spaces | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 1، دوره 16، شماره 1، فروردین 2025، صفحه 1-10 اصل مقاله (498.02 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.25200.2950 | ||
| نویسندگان | ||
| Manisha Devi1؛ Kuldip Raj1؛ Ayhan Esi* 2؛ Muhammed Aiyub3 | ||
| 1School of Mathematics Shri Mata Vaishno Devi University Katra-182320, J&K, India | ||
| 2Engineering Faculty Malatya Turgut Ozal University Malatya,44040, Turkey | ||
| 3Department of Mathematics, Bahrain University, P. O. Box-32038, Bahrain | ||
| تاریخ دریافت: 19 آبان 1400، تاریخ بازنگری: 20 شهریور 1402، تاریخ پذیرش: 22 شهریور 1402 | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Dirichlet-type space؛ Bloch-type spaces؛ generalized weighted composition operator؛ boundedness؛ compactness | ||
| مراجع | ||
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