Sharp Estimates for $p$-Adic Hardy, Hardy-Littlewood-Pólya Operators and Commutators

Details Sharp Estimates for $p$-Adic Hardy, Hardy-Littlewood-Pólya Operators and Commutators Sharp Estimates for $p$-Adic Hardy, Hardy-Littlewood-Pólya Operators and Commutators

2011-05-14

arxiv.org/abs/1105.2888v1

Mathematics

Functional Analysis

16pages

Scientific paper

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.

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