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The predual and John-Nirenberg inequalities on generalized BMO martingale spaces


Authors: Yong Jiao, Lian Wu, Anming Yang and Rui Yi
Journal: Trans. Amer. Math. Soc. 369 (2017), 537-553
MSC (2010): Primary 60G46; Secondary 60G42
DOI: https://doi.org/10.1090/tran/6657
Published electronically: April 14, 2016
MathSciNet review: 3557784
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Abstract: In this paper we introduce the generalized BMO martingale spaces by stopping time sequences, which enable us to characterize the dual spaces of martingale Hardy-Lorentz spaces $ H_{p,q}^s$ for $ 0<p\leq 1, 1<q<\infty $. Moreover, by duality we obtain a John-Nirenberg theorem for the generalized BMO martingale spaces when the stochastic basis is regular. We also extend the boundedness of fractional integrals to martingale Hardy-Lorentz spaces.


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Additional Information

Yong Jiao
Affiliation: School of Mathematics and Statistics, Central South University, Changsha 410085, People’s Republic of China
Email: jiaoyong@csu.edu.cn

Lian Wu
Affiliation: School of Mathematics and Statistics, Central South University, Changsha 410085, People’s Republic of China

Anming Yang
Affiliation: School of Mathematics and Statistics, Central South University, Changsha 410085, People’s Republic of China

Rui Yi
Affiliation: School of Mathematics and Statistics, Central South University, Changsha 410085, People’s Republic of China

DOI: https://doi.org/10.1090/tran/6657
Keywords: Predual, John-Nirenberg inequalities, generalized BMO spaces, martingale Hardy-Lorentz space, fractional integral
Received by editor(s): August 20, 2014
Received by editor(s) in revised form: January 9, 2015
Published electronically: April 14, 2016
Additional Notes: The first author was supported by NSFC (11471337), Hunan Provincial Natural Science Foundation(14JJ1004) and The International Postdoctoral Exchange Fellowship Program
Article copyright: © Copyright 2016 American Mathematical Society