Acta mathematica scientia, Series B >
COMMUTATORS OF GENERALIZED HARDY OPERATORS ON HOMOGENEOUS GROUPS
Received date: 2007-09-22
Revised date: 2008-05-26
Online published: 2010-05-20
Supported by
Supported by Chinese Universities Scientific Fund (2009RC0703 of BUPT) and the NNSF of China (10871024)
Let G be a homogeneous group. The author considers the boundedness of commutators generated by the generalized Hardy operators and CMO(G) functions on Herz spaces in the setting of homogeneous group. This article extends some known results.
Key words： Homogeneous group; CMO(G) function; Herz space; generalized Hardy operator
MO Hui-Xia . COMMUTATORS OF GENERALIZED HARDY OPERATORS ON HOMOGENEOUS GROUPS[J]. Acta mathematica scientia, Series B, 2010 , 30(3) : 897 -906 . DOI: 10.1016/S0252-9602(10)60087-2
[1] Hardy G H. Note on a theorem of Hilbert. Math Z, 1920, 6: 314--317
[2] Anderson K, Muckenhoupt B. Weighted weak type Hardy inequalities with application to Hilbert transforms and maximal functions. Studia Math, 1982, 72: 9--26
[3] Bliss G A. An integral inequality. J London Math Soc, 1930, 317(5): 40--46
[4] Edmunds D, Gurka P, Pick L. Compactness of Hardy type operators in weighted Banach function spaces. Studia Math, 1994, 109(1): 73--90
[5] Fu Z, Liu Z, Lu S, Wang H. Characterization for commutators of n-dimensional fractional Hardy operators. Sci China (Ser A-Math), 2007, 50(10): 1418--1426
[6] Fu Z, Lu S. Commutators of generalized Hardy operators. Math Nachr (in press)
[7] Folland G B, Stein E M. Hardy spaces on homogeneous groups. Math Notes 28. Princeton, NJ: Princeton Univ Press and Univ Tokyo Press, 1982
[8] Stein E M. Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals. Princeton, NJ: Univ Press, 1993
[9] Jiang Y. New Hardy spaces associated with Herz spaces and Beurling algebra on homogeneous groups. Acta Math Sinica (English Ser), 2002, 18(4): 661--670
[10] Muckenhoupt B. Hardy's inequality with weight. Studia Math, 1972, 44: 31--38
[11] Rakotondratsimba Y. On the boundedness of classical operator on weighted Lorentz spaces. Georgian Math J, 1998, 5: 177--200
[12] Xiao J. Lp and BMO bounds of weighted Hardy-Littlewood averages. J Math Anal Appl, 2001, 262: 600--666
[13] Kokilashvili V, Meskhi A. Two weighted inequalities for integral operators in Lorentz spaces defined on homogeneous groups. Georgian Math J, 1999, 6(1): 65--82
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