Norm of the Cesàro operator between some spaces of analytic functions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911255282843648 |
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| author | Ye, Shanli Ji, Bin Zheng, Qisong |
| author_facet | Ye, Shanli Ji, Bin Zheng, Qisong |
| contents | In this paper, we determine the exact norm of the Cesàro operator $\mathcal{C}$ on the Korenblum space $H^\infty_α$ for $0 < α\leq \frac12$ and on the logarithmically weighted space $H^\infty_{α,\log}$ for $0 < α< 1$. Moreover, we compute its norm when acting from $H^\infty_{α,\log}$ to $H^\infty_α$. Finally, we establish lower and upper bounds for the norm of $\mathcal{C}$ on the $α$-Bloch space $\mathcal{B}^α$ for $α> 1$, and from the Hardy space $H^\infty$ to $\mathcal{B}^α$ for $α\geq 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01152 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Norm of the Cesàro operator between some spaces of analytic functions Ye, Shanli Ji, Bin Zheng, Qisong Functional Analysis Complex Variables 47A30, 47B38, 47B91, 30H05, 30H30, 30H99 In this paper, we determine the exact norm of the Cesàro operator $\mathcal{C}$ on the Korenblum space $H^\infty_α$ for $0 < α\leq \frac12$ and on the logarithmically weighted space $H^\infty_{α,\log}$ for $0 < α< 1$. Moreover, we compute its norm when acting from $H^\infty_{α,\log}$ to $H^\infty_α$. Finally, we establish lower and upper bounds for the norm of $\mathcal{C}$ on the $α$-Bloch space $\mathcal{B}^α$ for $α> 1$, and from the Hardy space $H^\infty$ to $\mathcal{B}^α$ for $α\geq 1$. |
| title | Norm of the Cesàro operator between some spaces of analytic functions |
| topic | Functional Analysis Complex Variables 47A30, 47B38, 47B91, 30H05, 30H30, 30H99 |
| url | https://arxiv.org/abs/2511.01152 |