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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.17446 |
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| _version_ | 1866916141034635264 |
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| author | Mas, Alejandro Merchán, Noel de la Rosa, Elena |
| author_facet | Mas, Alejandro Merchán, Noel de la Rosa, Elena |
| contents | Let $\mathbb{D}$ denote the unit disc in $\mathbb{C}$. We define the generalized Cesàro operator as follows
$$
C_ω(f)(z)=\int_0^1 f(tz)\left(\frac{1}{z}\int_0^z B^ω_t(u)\,du\right)\,ω(t)dt,$$
where $\{B^ω_ζ\}_{ζ\in\mathbb{D}}$ are the reproducing kernels of the Bergman space $A^2_ω$ induced by a radial weight $ω$ in the unit disc $\mathbb{D}$. We study the action of the operator $C_ω$ on weighted Hardy spaces of analytic functions $\mathcal{H}_γ$, $γ>0$ and on general weighted Bergman spaces $A^2_μ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17446 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Cesàro operator acting on Hilbert spaces of analytic functions Mas, Alejandro Merchán, Noel de la Rosa, Elena Complex Variables Let $\mathbb{D}$ denote the unit disc in $\mathbb{C}$. We define the generalized Cesàro operator as follows $$ C_ω(f)(z)=\int_0^1 f(tz)\left(\frac{1}{z}\int_0^z B^ω_t(u)\,du\right)\,ω(t)dt,$$ where $\{B^ω_ζ\}_{ζ\in\mathbb{D}}$ are the reproducing kernels of the Bergman space $A^2_ω$ induced by a radial weight $ω$ in the unit disc $\mathbb{D}$. We study the action of the operator $C_ω$ on weighted Hardy spaces of analytic functions $\mathcal{H}_γ$, $γ>0$ and on general weighted Bergman spaces $A^2_μ$. |
| title | Generalized Cesàro operator acting on Hilbert spaces of analytic functions |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2402.17446 |