A characterization of λ-central BMO space

Abstract

We give a characterization of the λ-central BMO space via the boundedness of commutators of n-dimensional Hardy operators.

Keywords

λ-central BMO space / n-dimensional Hardy operator / commutator

References

[1] Alvarez J, Guzmián-Partida M, Lakey J. Spaces of bounded λ-central mean oscillation, Morrey spaces, and λ-central Carleson measures. Collect Math, 2000, 51: 1-47

[2] Bastero J, Milman M, Ruiz F J. Commutators of the maximal and sharp functions. Proc Amer Math Soc, 2000, 128: 3329-3334

[3] Chen Y Z, Lau K S. Some new classes of Hardy spaces. J Funct Anal, 1989, 84: 255-278

[4] Christ M, Grafakos L. Best constants for two nonconvolution inequalities. Proc Amer Math Soc, 1995, 123: 1687-1693

[5] Coifman R R, Rochberg R, Weiss G. Factorization theorems for Hardy spaces in several variables. Ann Math, 1976, 103: 611-635

[6] Ding Y, Lu S Z, Yabuta K. On commutators of Marcinkiewicz integrals with rough kernel. J Math Anal Appl, 2002, 275: 60-68

[7] Faris W. Weak Lebesgue spaces and quantum mechanical binding. Duke Math J, 1976, 43: 365-373

[8] Fefferman C. Characterization of bounded mean oscillation. Bull Amer Math Soc, 1971, 77: 587-588

[9] Fu Z W, Liu Z G, Lu S Z, Wang H B. Characterization for commutators of n-dimensional fractional Hardy operators. Sci China Ser A, 2007, 50: 1418-1426

[10] Fu Z W, Lu S Z. Commutators of generalized Hardy operators. Math Nachr, 2009, 282: 832-845

[11] Garcì-Cuerva J. Hardy spaces and Beurling algebras. J Lond Math Soc, 1989, 39: 499-513

[12] Hardy G H, Littlewood J, Póya G. Inequalities. 2nd ed. London/New York: Cambridge University Press, 1952

[13] Komori Y. Notes on commutators of Hardy operators. Int J Pure Appl Math, 2003, 7: 329-334

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

[15] Lu S Z, Yang D C. The central BMO spaces and Littlewood-Paley operators. Approx Theory Appl, 1995, 11: 72-94

[16] Meng Y, Yang D C. Boundedness of commutators with Lipschitz functions in nonhomogeneous spaces. Taiwanese J Math, 2006, 10: 1443-1464

[17] Segovia C, Torrea J L. Vector-valued commutators and applications. Indiana Univ Math J, 1989, 38: 959-971

[18] Tang C Q, Li Q G, Ma B L. Commutators of fractional integral operator associated to a nondoubling measures on metric spaces. Taiwanese J Math, 2009, 13: 1043-1052

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