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 inScience China. Mathematics Vol. 55; no. 10; pp. 1977 - 1990
Main Authors Zhao, FaYou, Fu, ZunWei, Lu, ShanZhen
Format Journal Article
LanguageEnglish
Published Heidelberg SP Science China Press 01.10.2012
Subjects
Applications of Mathematics
Campanato空间
China
Commutators
Estimates
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
generalized Hardy operator
commutator
47B38
26D10
Campanato space
sharp bound
26D15
Hardy space
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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.
Bibliography: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.
sharp bound, generalized Hardy operator, commutator, Campanato space, Hardy space
11-1787/N
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-012-4465-0