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(M) over center dotO) 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 (C-1(Q(p)(n))) with compact support.