The norm of the Hilbert matrix operator on Bergman spaces
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917245164191744 |
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| author | Bao, Guanlong Tian, Liu Wulan, Hasi |
| author_facet | Bao, Guanlong Tian, Liu Wulan, Hasi |
| contents | Karapetrović conjectured that the norm of the Hilbert matrix operator on the Bergman space $A^p_α$ is equal to $π/\sin((2+α)π/p)$ when $-1<α<p-2$. In this paper, we provide a proof of this conjecture for $0\leq α\leq \frac{6p^3-29p^2+17p-2+2p\sqrt{6p^2-11p+4}}{(3p-1)^2}$, and this range of $α$ improves the best known result when $α>\frac{1}{47}$ and $α\not=1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13672 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The norm of the Hilbert matrix operator on Bergman spaces Bao, Guanlong Tian, Liu Wulan, Hasi Complex Variables Functional Analysis Karapetrović conjectured that the norm of the Hilbert matrix operator on the Bergman space $A^p_α$ is equal to $π/\sin((2+α)π/p)$ when $-1<α<p-2$. In this paper, we provide a proof of this conjecture for $0\leq α\leq \frac{6p^3-29p^2+17p-2+2p\sqrt{6p^2-11p+4}}{(3p-1)^2}$, and this range of $α$ improves the best known result when $α>\frac{1}{47}$ and $α\not=1$. |
| title | The norm of the Hilbert matrix operator on Bergman spaces |
| topic | Complex Variables Functional Analysis |
| url | https://arxiv.org/abs/2601.13672 |