In this note we study the boundedness of \(p\)-adic fractional integral operator with rough kernels on \(p\)-adic Herz spaces. Moreover, we establish Lipschitz estimates for commutators of \(p\)-adic fractional integral operator with rough kernels on Herz spaces. In addition, we also obtain central bounded mean oscillations\((C{\dot{M}}O)\) estimate for commutators of \(p\)-adic fractional integral operator with rough kernels on \(p\)-adic Herz spaces. As an application, we characterize \(p\)-adic Herz space in terms of wavelets in continuously differentiable functions \(({\mathcal {C}}^{1}({\mathbb {Q}}_p^n))\) with compact support.

在本笔记中，我们研究了在\(p\) -adic Herz 空间上具有粗糙核的\(p\) -adic 分数积分算子的有界性。此外，我们建立了在 Herz 空间上具有粗糙核的\(p\) -adic 分数积分算子的交换子的 Lipschitz 估计。此外，我们还获得了\(p\) -adic 分数积分算子的交换子的中心有界平均振荡\((C{\dot{M}}O)\)估计，在\(p \ ) -adic上具有粗糙内核赫兹空间。作为一个应用，我们用连续可微函数\(({\mathcal {C}}^{1}({\mathbb {Q}}_p^n))中的小波来表征\(p\) -adic Herz 空间\)与紧凑的支持。