Integral Operators on Fractional Cesàro--Morrey Spaces over $\mathbb{Q}_p$

Abstract

In this paper, we introduce fractional Cesàro--Morrey function spaces over $p$-adic fields and investigate their fundamental properties. We first study the behavior of dilation operators on these spaces and establish a Minkowski-type integral inequality. We then prove the boundedness of $p$-adic Hardy--Hilbert--type integral operators on fractional Cesàro--Morrey function spaces. As an applications, we derive the $p$-adic Hardy inequality, the Hilbert inequality, and the Hardy--Littlewood--Pólya inequality. Finally, we establish the boundedness of the Erdélyi--Kober fractional integral operator and the Hadamard fractional integral operator on these spaces.