Norm of the Hilbert matrix operator between some spaces of analytic functions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909358893301760 |
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| author | Hu, Hao Ye, Shanli |
| author_facet | Hu, Hao Ye, Shanli |
| contents | In this paper, we calculate the exact value of the norm of the Hilbert matrix operator $\mathcal{H}$ from the logarithmically weighted Korenblum space $H^\infty_{α,\log}$ into Korenblum space $H^\infty_α$, and from the Hardy space $H^\infty$ to the classical Bloch space $\mathcal{B}$. Furthermore, we compute the precise value of the norm on the logarithmically weighted Korenblum space $H^\infty_{α,\log}$, and obtain both the lower and upper bounds of the norm on $α$-Bloch space $\mathcal{B}^α$. Finally, in the context of mapping from the Korenblum space $H^\infty_α$ to the $(α+1)$-Bloch space $\mathcal{B}^{α+1}$, we establish the norm of $\mathcal{H}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16598 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Norm of the Hilbert matrix operator between some spaces of analytic functions Hu, Hao Ye, Shanli Functional Analysis In this paper, we calculate the exact value of the norm of the Hilbert matrix operator $\mathcal{H}$ from the logarithmically weighted Korenblum space $H^\infty_{α,\log}$ into Korenblum space $H^\infty_α$, and from the Hardy space $H^\infty$ to the classical Bloch space $\mathcal{B}$. Furthermore, we compute the precise value of the norm on the logarithmically weighted Korenblum space $H^\infty_{α,\log}$, and obtain both the lower and upper bounds of the norm on $α$-Bloch space $\mathcal{B}^α$. Finally, in the context of mapping from the Korenblum space $H^\infty_α$ to the $(α+1)$-Bloch space $\mathcal{B}^{α+1}$, we establish the norm of $\mathcal{H}$. |
| title | Norm of the Hilbert matrix operator between some spaces of analytic functions |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2410.16598 |