Higher-order Volterra-type integral operator on Hardy and Bergman spaces
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910117964808192 |
|---|---|
| author | Kargar, Rahim |
| author_facet | Kargar, Rahim |
| contents | We investigate the higher-order Volterra-type integral operator $T_{g,n}$ on the unit disk, defined for $n\in\mathbb N$ by \[ T_{g,n}[f](z) := \underbrace{\int_{0}^{z}\int_{0}^{t_1}\cdots\int_{0}^{t_{n-1}}}_{n\ \text{times}} f(t_n)g'(t_n)\,dt_n\cdots dt_1,\quad z\in\mathbb D, \] where $f$ and $g$ are analytic in the unit disk $\mathbb D$. We establish sharp norm and essential norm estimates, and give complete characterizations of boundedness and compactness of $T_{g,n}$ on Hardy spaces $H^p$ and weighted Bergman spaces $A_α^p$, in terms of (vanishing) Carleson measure conditions determined by $|g'|$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16412 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher-order Volterra-type integral operator on Hardy and Bergman spaces Kargar, Rahim Complex Variables 47B38, 47B01 We investigate the higher-order Volterra-type integral operator $T_{g,n}$ on the unit disk, defined for $n\in\mathbb N$ by \[ T_{g,n}[f](z) := \underbrace{\int_{0}^{z}\int_{0}^{t_1}\cdots\int_{0}^{t_{n-1}}}_{n\ \text{times}} f(t_n)g'(t_n)\,dt_n\cdots dt_1,\quad z\in\mathbb D, \] where $f$ and $g$ are analytic in the unit disk $\mathbb D$. We establish sharp norm and essential norm estimates, and give complete characterizations of boundedness and compactness of $T_{g,n}$ on Hardy spaces $H^p$ and weighted Bergman spaces $A_α^p$, in terms of (vanishing) Carleson measure conditions determined by $|g'|$. |
| title | Higher-order Volterra-type integral operator on Hardy and Bergman spaces |
| topic | Complex Variables 47B38, 47B01 |
| url | https://arxiv.org/abs/2512.16412 |