  In this paper we get the sharp estimates of the $p$-adic Hardy and
Hardy-Littlewood-P\'olya operators on $L^q(|x|^{\alpha}_pdx)$. Also, we prove
that the commutators generated by the $p$-adic Hardy operators
(Hardy-Littlewood-P\'olya operators) and the central BMO functions are bounded
on $L^q(|x|^{\alpha}_pdx)$, more generally, on Herz spaces.
