On the discrete Hilbert-type operators
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918131070402560 |
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| author | Jin, Jianjun |
| author_facet | Jin, Jianjun |
| contents | Recently, Bansah and Sehba studied in [3] the boundedness of a family of Hilbert-type integral operators, where they characterized the $L^{p}-L^{q}$ boundedness of the operators for $1\leq p\leq q\leq \infty$. In this paper, we deal with the corresponding discrete Hilbert-type operators acting on the weighted sequence spaces. We establish some sufficient and necessary conditions for the $l^{p}-l^{q}$ boundedness of the operators for $1\leq p\leq q\leq \infty$. We find out that the conditions of the boundedness of discrete Hilbert-type operators are different from those of the boundedness of Hilbert-type integral operators. Also, for some special cases, we obtain sharp norm estimates for discrete Hilbert-type operators. Finally, it is pointed out that certain extensions of the theorems given in [3] can be established by using our different arguments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22972 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the discrete Hilbert-type operators Jin, Jianjun Functional Analysis Classical Analysis and ODEs 47B37, 47A30 Recently, Bansah and Sehba studied in [3] the boundedness of a family of Hilbert-type integral operators, where they characterized the $L^{p}-L^{q}$ boundedness of the operators for $1\leq p\leq q\leq \infty$. In this paper, we deal with the corresponding discrete Hilbert-type operators acting on the weighted sequence spaces. We establish some sufficient and necessary conditions for the $l^{p}-l^{q}$ boundedness of the operators for $1\leq p\leq q\leq \infty$. We find out that the conditions of the boundedness of discrete Hilbert-type operators are different from those of the boundedness of Hilbert-type integral operators. Also, for some special cases, we obtain sharp norm estimates for discrete Hilbert-type operators. Finally, it is pointed out that certain extensions of the theorems given in [3] can be established by using our different arguments. |
| title | On the discrete Hilbert-type operators |
| topic | Functional Analysis Classical Analysis and ODEs 47B37, 47A30 |
| url | https://arxiv.org/abs/2505.22972 |