RESEARCH ARTICLE

Spaces of type BLO on non-homogeneous metric measure

  • Haibo LIN 1 ,
  • Dachun YANG , 2
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  • 1. College of Science, China Agricultural University, Beijing 100083, China
  • 2. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex systems, Ministry of Education, Beijing 100875, China

Received date: 11 Nov 2010

Accepted date: 06 Dec 2010

Published date: 01 Apr 2011

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

Let (,d,μ) be a metric measure space satisfying the so-called upper doubling condition and the geometrically doubling condition. In this paper, we introduce the space RBLO(μ) and prove that it is a subset of the known space RBMO(μ) in this context. Moreover, we establish several useful characterizations for the space RBLO(μ). As an application, we obtain the boundedness of the maximal Calderón-Zygmund operators from L(μ) to RBLO(μ).

Cite this article

Haibo LIN , Dachun YANG . Spaces of type BLO on non-homogeneous metric measure[J]. Frontiers of Mathematics in China, 2011 , 6(2) : 271 -292 . DOI: 10.1007/s11464-011-0098-9

1
Benett C. Another characterization of BLO. Proc Amer Math Soc, 1982, 85: 552-556

2
Coifman R R, Rochberg R. Another characterization of BMO. Proc Amer Math Soc, 1980, 79: 249-254

3
Coifman R R, Weiss G. Analyse Harmonique Non-commutative sur Certains Espaces Homogènes. Lecture Notes in Math, 242, Berlin: Springer, 1971

4
Coifman R R, Weiss G. Extensions of Hardy spaces and their use in analysis. Bull Amer Math Soc, 1977, 83: 569-645

DOI

5
Hajłasz P, Koskela P. Sobolev met Poincaré. Mem Amer Math Soc, Vol 145, No 688. Providence: Amer Math Soc, 2000

6
Heinenon J. Lectures on Analysis on Metric Spaces. New York: Springer-Verlag, 2001

7
Hu Guoen, Yang Dachun, Yang Dongyong. h1, bmo, blo and Littlewood-Paley g-functions with non-doubling measures. Rev Mat Ibero, 2009, 25: 595-667

8
Hytönen T. A framework for non-homogeneous analysis on metric spaces, and the RBMO space of Tolsa. Publ Mat, 2010, 54: 485-504

9
Hytönen T, Liu Suile, Yang Dachun, Yang Dongyong. Boundedness of Calderón-Zygmund operators on non-homogeneous metric measure spaces. Canad J Math (to appear) or arXiv: 1011.2937

10
Hytönen T, Martikainen H. Non-homogeneous Tb theorem and random dyadic cubes on metric measure spaces. arXiv: 0911.4387

11
Hytönen T, Yang Dachun, Yang Dongyong. The Hardy space H1 on non-homogeneous metric spaces. arXiv: 1008.3831

12
Jiang Y. Spaces of type BLO for non-doubling measures. Proc Amer Math Soc, 2005, 133: 2101-2107

DOI

13
Leckband M A. Structure results on the maximal Hilbert transform and two-weight norm inequalities. Indiana Univ Math J, 1985, 34: 259-275

DOI

14
Luukkainen J, Saksman E. Every complete doubling metric space carries a doubling measure. Proc Amer Math Soc, 1998, 126: 531-534

DOI

15
Nazarov F, Treil S, Volberg V. The Tb-theorem on non-homogeneous spaces. Acta Math, 2003, 190: 151-239

DOI

16
Stein E M. Singular integral, harmonic functions, and differentiability properties of functions of several variables. In: Calderón A P, ed. Singular Integrals. Proc Symp Pure Math, 10. Providence: Amer Math Soc, 1967, 316-335

17
Tolsa X. BMO, H1 and Calderón-Zygmund operators for non doubling measures. Math Ann, 2001, 319: 89-149

DOI

18
Tolsa X. Painlevé’s problem and the semiadditivity of analytic capacity. Acta Math, 2003, 190: 105-149

DOI

19
Tolsa X. Analytic capacity and Calderón-Zygmund theory with non doubling measures. Seminar of Mathematical Analysis. Colecc Abierta, 71. Seville: Univ Sevilla Secr Publ, 2004, 239-271

20
Volberg A, Wick B D. Bergman-type singular operators and the characterization of Carleson measures for Besov-Sobolev spaces on the complex ball. Amer J Math (to appear) or arXiv: 0910.1142

21
Wu J. Hausdorff dimension and doubling measures on metric spaces. Proc Amer Math Soc, 1998, 126: 1453-1459

DOI

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