On the discrete Hilbert-type operators

2025/05/29 by Jin, Jianjun
#47A30 #47B37 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2505.22972

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≤ p≤ q≤ ∞. 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≤ p≤ q≤ ∞. 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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