Some estimates for $$p$$-adic fractional integral operator and its commutators on $$p$$-adic Herz spaces with rough kernels

Abstract

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.