In this paper we get the sharp estimates of the p-adic Hardy and Hard^Littlewood-Pdlya operators on L^q (|x|apdx). Also, we prove that the commutators generated by the p-adic Hardy operators (Hardy-Littlewood-Pdlya operators) and the central BMO functions are bounded on L^q (|x|apdx), more generally, on Herz spaces.