RESEARCH ARTICLE

A characterization of λ-central BMO space

  • Fayou ZHAO , 1 ,
  • Shanzhen LU 2
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  • 1. Department of Mathematics, Shanghai University, Shanghai 200444, China
  • 2. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

Received date: 17 Mar 2011

Accepted date: 27 Sep 2012

Published date: 01 Feb 2013

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

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

Cite this article

Fayou ZHAO , Shanzhen LU . A characterization of λ-central BMO space[J]. Frontiers of Mathematics in China, 2013 , 8(1) : 229 -238 . DOI: 10.1007/s11464-012-0251-0

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

DOI

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

DOI

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

DOI

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

DOI

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

DOI

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

DOI

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

DOI

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

DOI

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

DOI

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

DOI

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

DOI

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

DOI

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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