分数次 Hardy算子多线性交换子的有界性

Abstract

Abstract:

In this paper, the boundedness of the multilinear commutator H_{e, b} generated by an n-dimensional fractional Hardy operator and BMO function is established on the Lebesgue space, the homogenous Herz space K_q^{α, p}(Rⁿ) and the homogenous Morrey-Herz
space MK_{p, q}, ^α, λ(Rⁿ).

Key words: Hardy operator, Morrey-Herz space, Commutator, BMO function

CLC Number:

42B20

Cite this article

WU Jiang-Long. Boundedness of Multilinear Commutators of Fractional Hardy Operators[J].Acta mathematica scientia,Series A, 2011, 31(4): 1055-1062.

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References

[1] Hardy G. Note on a theorem of Hilbert. Mathematische Zeitschrift, 1920, 6: 314--317

[2] Hardy G, Littlewood J, Polya G. Inequalities. Cambridge: Cambridge Univeristy Press,1952

[3] Anderson K, Muckenhoupt B. Weighted weak type Hardy inequalities with application to Hilbert transforms and maximal functions. Studia Math, 1982, 72: 9--26

[4] Sawyer E. Weighted Lebesgue and Lorentz norm inequalities for the Hardy operator. Trans Amer Math Soc, 1984, 1: 329--337

[5] Golubov B. Boundedness of the Hardy and the Hardy-Littlewood operators in the spaces ReH¹ and BMO. Sbornik Mathematics, 1997, 188: 1041--1054

[6] Long S, Wang J. Commutators of Hardy operators. J Math Anal Appl, 2002, 274: 626--644

[7] Chirst M, Grafakos L. Best constants for two non-convolution inequalities. Proc Amer Math Soc, 1995, 123: 1687--1693

[8] 傅尊伟, 刘宗光, 陆善镇, 等. n维分数次Hardy算子交换子的特征. 中国科学A辑, 2007, 37: 651--659

[9] Zhang Q, Fu Z. Lipschitz estimates for commutators of n-dimensional fractional Hardy operators. Communications in Mathematical Research, 2009, 25: 241--245

[10] Pé}rez C, Trujillo-Gonz\'{a}lez R. Sharp weighted estimates for multilinear commutators. J London Math Soc, 2002, 65: 672--692

[11] Lu S, Xu L. Boundedness of rough singular integral operators on the homogeneous Morrey-Herz spaces. Hokkaido Mathematical Journal, 2005, 34: 299--314

[12] Lu S, Tang L, Yang D. Boundedness of commutators on homogeneous Herz spaces. Sci China Ser A, 1998, 41: 1023--1033

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Boundedness of Multilinear Commutators of Fractional Hardy Operators

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