Annales Academiĉ Scientiarum Fennicĉ
Mathematica
Volumen 38, 2013, 3-27

A NEW CHARACTERIZATION OF REGULARIZED BMO SPACES ON NON-HOMOGENEOUS SPACES AND ITS APPLICATIONS

Guoen Hu, Yan Meng and Dachun Yang

Zhengzhou Information Science and Technology Institute, Department of Applied Mathematics
P.O. Box 1001-747, Zhengzhou 450002, P.R. China; guoenxx 'at' yahoo.com.cn

Renmin University of China, School of Information
Beijing 100872, P.R. China; mengyan 'at' ruc.edu.cn

Beijing Normal University, School of Mathematical Sciences
Laboratory of Mathematics and Complex Systems, Ministry of Education
Beijing 100875, P.R. China; dcyang 'at' bnu.edu.cn

Abstract. Let (X,d,\mu) be a metric measure space and satisfy the so-called upper doubling condition and the geometrically doubling condition. Under this assumption, in this paper, the authors establish a new characterization of the space RBMO(\mu). As applications, the authors prove that the L^p(\mu)-boundedness with p \in (1,\infty) of the Calderón-Zygmund operator is equivalent to its various endpoint estimates.

2010 Mathematics Subject Classification: Primary 42B20; Secondary 42B25, 42B35, 42B30.

Key words: RBMO(\mu), Calderón-Zygmund operator, upper doubling measure, geometrically doubling, metric measure space.

Reference to this article: G. Hu, Y. Meng and D. Yang: A new characterization of regularized BMO spaces on non-homogeneous spaces and its applications. Ann. Acad. Sci. Fenn. Math. 38 (2013), 3-27.

Full document as PDF file

doi:10.5186/aasfm.2013.3809

Copyright © 2013 by Academia Scientiarum Fennica