Endpoint estimates for n-dimensional Hardy operators and their commutators

In this paper, the sharp bound for the weak-type （1, 1） inequality for the n-dimensional Hardy operator is obtained. Moreover, the precise norms of generalized Hardy operators on the type of Campanato spaces are worked out. As applications, the corresponding norms of the Riemann-Liouville integral o...

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Bibliographic Details
Published in:Science China. Mathematics 2012-10, Vol.55 (10), p.1977-1990
Main Authors: Zhao, FaYou, Fu, ZunWei, Lu, ShanZhen
Format: Article
Language:English
Subjects:
Applications of Mathematics
Astronomy
Campanato空间
China
Commutators
Estimates
Functions (mathematics)
Hardy空间
Hardy算子
Inequalities
Lebesgue空间
Mathematical analysis
Mathematics
Mathematics and Statistics
Norms
Operators
换向器
端点估计
运营商
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Summary:In this paper, the sharp bound for the weak-type （1, 1） inequality for the n-dimensional Hardy operator is obtained. Moreover, the precise norms of generalized Hardy operators on the type of Campanato spaces are worked out. As applications, the corresponding norms of the Riemann-Liouville integral operator and the n-dimensional Hardy operator are deduced. It is also proved that the n-dimensional Hardy operator maps from the Hardy space into the Lebesgue space. The endpoint estimate for the commutator generated by the Hardy operator and the （central） BMO function is also discussed.
ISSN:1674-7283
1006-9283
1869-1862
DOI:10.1007/s11425-012-4465-0