Optimal domain of Volterra operators in Korenblum spaces
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914415101607936 |
|---|---|
| author | Albanese, Angela A. Bonet, José Ricker, Werner J. |
| author_facet | Albanese, Angela A. Bonet, José Ricker, Werner J. |
| contents | The aim of this article is to study the largest domain space $[T,X]$, whenever it exists, of a given continuous linear operator $T\colon X\to X$, where $X\subseteq H(\mathbb{D})$ is a Banach space of analytic functions on the open unit disc $\mathbb{D}\subseteq \mathbb{C}$. That is, $[T,X]\subseteq H(\mathbb{D})$ is the \textit{largest} Banach space of analytic functions containing $X$ to which $T$ has a continuous, linear, $X$-valued extension $T\colon [T,X]\to X$. The class of operators considered consists of generalized Volterra operators $T$ acting in the Korenblum growth Banach spaces $X:=A^{-γ}$, for $γ>0$. Previous studies dealt with the classical Cesàro operator $T:=C$ acting in the Hardy spaces $H^p$, $1\leq p<\infty$, \cite{CR}, \cite{CR1}, in $A^{-γ}$, \cite{ABR-R}, and more recently, generalized Volterra operators $T$ acting in $X:=H^p$, \cite{BDNS}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00755 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal domain of Volterra operators in Korenblum spaces Albanese, Angela A. Bonet, José Ricker, Werner J. Functional Analysis Primary 46E15, 47B38, Secondary 46E10, 47A10, 47A16, 47A35 47A16, 47A35 The aim of this article is to study the largest domain space $[T,X]$, whenever it exists, of a given continuous linear operator $T\colon X\to X$, where $X\subseteq H(\mathbb{D})$ is a Banach space of analytic functions on the open unit disc $\mathbb{D}\subseteq \mathbb{C}$. That is, $[T,X]\subseteq H(\mathbb{D})$ is the \textit{largest} Banach space of analytic functions containing $X$ to which $T$ has a continuous, linear, $X$-valued extension $T\colon [T,X]\to X$. The class of operators considered consists of generalized Volterra operators $T$ acting in the Korenblum growth Banach spaces $X:=A^{-γ}$, for $γ>0$. Previous studies dealt with the classical Cesàro operator $T:=C$ acting in the Hardy spaces $H^p$, $1\leq p<\infty$, \cite{CR}, \cite{CR1}, in $A^{-γ}$, \cite{ABR-R}, and more recently, generalized Volterra operators $T$ acting in $X:=H^p$, \cite{BDNS}. |
| title | Optimal domain of Volterra operators in Korenblum spaces |
| topic | Functional Analysis Primary 46E15, 47B38, Secondary 46E10, 47A10, 47A16, 47A35 47A16, 47A35 |
| url | https://arxiv.org/abs/2502.00755 |