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-Pólya operators on L q (| x | p α dx ). Also, we prove that the commutators generated by the p -adic Hardy operators (Hardy-Littlewood-Pólya operators) and the central BMO functions are bounded on L q (| x | p α dx ),...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2013, Vol.29 (1), p.137-150
Main Authors: Fu, Zun Wei, Wu, Qing Yan, Lu, Shan Zhen
Format: Article
Language:English
Subjects:
Commutators
Estimates
Estimating techniques
Harmonic analysis
Mathematical analysis
Mathematics
Mathematics and Statistics
Operators
Studies
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Summary:In this paper we get the sharp estimates of the p -adic Hardy and Hardy-Littlewood-Pólya operators on L q (| x | p α dx ). Also, we prove that the commutators generated by the p -adic Hardy operators (Hardy-Littlewood-Pólya operators) and the central BMO functions are bounded on L q (| x | p α dx ), more generally, on Herz spaces.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-012-0695-x