<正>In this paper we get the sharp estimates of the p-adic Hardy and Hardy-Littlewood -Pólya operators on Lq(|x|pαdx).Also,we prove that the commutators generated by the padic Hardy operators(Hardy-Littlewood-Pólya operators) and the central BMO functions are bounded on Lq(|x|pαdx),more generally,on Herz spaces.