Generalized Hilbert operators acting on weighted sequence spaces

2025/04/28 by Jin, Jianjun
#26D15 #47A30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2504.19743

Abstract

In this paper we introduce and study a new kind of generalized Hilbert operators, induced by a finite positive Borel measure on (0,1), acting on weighted sequence spaces. We establish a sufficient and necessary condition for the boundedness of these operators. These results extend some related ones obtained recently in [Bull London Math Soc, 55 (2023), no. 6, 2598-2610].

Citations

• On the Hilbert matrix operator: a brief survey
• Generalized Hilbert matrix operators acting on Bergman spaces
• Generalized Hilbert operators arising from Hausdorff matrices
• A variant of Hilbert's inequality and the norm of the Hilbert Matrix on K^p
• Exact essential norm of generalized Hilbert matrix operators on classical analytic function spaces
• On the exact value of the norm of the Hilbert matrix operator on\n weighted Bergman spaces
• Generalized Hilbert operators on weighted Bergman spaces

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