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arXiv · 2505.22972

On the discrete Hilbert-type operators

Jianjun Jin
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Abstract

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.

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Jianjun Jin. 2025-05-29. On the discrete Hilbert-type operators. https://arxiv.org/abs/2505.22972

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