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

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.