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

Sharp Estimates for $p$-Adic Hardy, Hardy-Littlewood-P\'olya Operators and Commutators