Sharp Estimates of p-Adic Hardy and Hardy–Littlewood–Pólya Operators

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