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

Authors
Type
Preprint
Publication Date
May 14, 2011
Submission Date
May 14, 2011
Source
arXiv
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.