Norm of the Hilbert matrix operator on logarithmically weighted Bloch and Hardy spaces
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918197792342016 |
|---|---|
| author | Ye, Shanli Zheng, Qisong |
| author_facet | Ye, Shanli Zheng, Qisong |
| contents | In this paper, we compute the exact value of the norm of the Hilbert matrix operator $\mathcal{H}$ acting from the classical Bloch space $\mathcal{B}$ into the logarithmically weighted Bloch space $\mathcal{B}_{\log}$, and show that it equals $\frac{3}{2}$; we also find that the norm from the space of bounded analytic functions $H^\infty$ into the logarithmically weighted Hardy space $H^{\infty}_{\log}$ is $1$. Furthermore, we establish both lower and upper bounds for the norm of $\mathcal{H}$ when it maps from the $α$-Bloch space $\mathcal{B}^α$ into the logarithmically weighted $\mathcal{B}^α_{\log}$ with $1 <α< 2$, and from the Hardy space $H^{1}$ into the logarithmically weighted Hardy space $H^{1}_{\log}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23314 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Norm of the Hilbert matrix operator on logarithmically weighted Bloch and Hardy spaces Ye, Shanli Zheng, Qisong Functional Analysis Complex Variables 47A30, 47B38, 47B91, 30H30, 30H05, 30H10 In this paper, we compute the exact value of the norm of the Hilbert matrix operator $\mathcal{H}$ acting from the classical Bloch space $\mathcal{B}$ into the logarithmically weighted Bloch space $\mathcal{B}_{\log}$, and show that it equals $\frac{3}{2}$; we also find that the norm from the space of bounded analytic functions $H^\infty$ into the logarithmically weighted Hardy space $H^{\infty}_{\log}$ is $1$. Furthermore, we establish both lower and upper bounds for the norm of $\mathcal{H}$ when it maps from the $α$-Bloch space $\mathcal{B}^α$ into the logarithmically weighted $\mathcal{B}^α_{\log}$ with $1 <α< 2$, and from the Hardy space $H^{1}$ into the logarithmically weighted Hardy space $H^{1}_{\log}$. |
| title | Norm of the Hilbert matrix operator on logarithmically weighted Bloch and Hardy spaces |
| topic | Functional Analysis Complex Variables 47A30, 47B38, 47B91, 30H30, 30H05, 30H10 |
| url | https://arxiv.org/abs/2510.23314 |