Boundedness of $p$-adic Hardy--Hilbert and Erd\'elyi--Kober fractional integral operators on $p$-adic Ces\`aro function Spaces

Rishabh Saini; Qaiser Jahan; Salman Ashraf

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arXiv · 2606.25428

Boundedness of $p$-adic Hardy--Hilbert and Erd\'elyi--Kober fractional integral operators on $p$-adic Ces\`aro function Spaces

Rishabh Saini·Qaiser Jahan·Salman Ashraf

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Abstract

In this paper, we introduce Ces\`aro function spaces over $p$-adic fields and investigate their fundamental properties, such as the dilation operator and the Minkowski-type integral inequality. We establish boundedness result for $p$-adic Hardy--Hilbert-type integral operators acting on $p$-adic Ces\`aro function spaces, and as an application we derive $p$-adic analogue of the Hardy inequality, the Hilbert inequality, and the Hardy-Littlewood-P\'{o}lya inequality. Furthermore, we define the $p$-adic analogue of the Erd\'elyi--Kober fractional integral operators and prove their boundedness on $p$-adic Ces\`aro function spaces with the help of the obtained boundedness result.

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Rishabh Saini, Qaiser Jahan, Salman Ashraf. 2026-06-24. Boundedness of $p$-adic Hardy--Hilbert and Erd\'elyi--Kober fractional integral operators on $p$-adic Ces\`aro function Spaces. https://arxiv.org/abs/2606.25428

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