BURKHOLDER-GUNDY-DAVIS INEQUALITY IN MARTINGALE HARDY SPACES WITH VARIABLE EXPONENT

doi:10.1016/S0252-9602(18)30805-1

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (4): 1151-1162.doi: 10.1016/S0252-9602(18)30805-1

BURKHOLDER-GUNDY-DAVIS INEQUALITY IN MARTINGALE HARDY SPACES WITH VARIABLE EXPONENT

刘培德, 王茂发

School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

收稿日期:2017-06-30 修回日期:2017-12-07 出版日期:2018-08-25 发布日期:2018-08-25
通讯作者: Peide LIU,E-mail:pdliu@whu.edu.cn E-mail:pdliu@whu.edu.cn
作者简介:Maofa WANG,E-mail:mfwang.math@whu.edu.cn
基金资助:
The first author was supported by NSFC (11471251). The second author was supported by NSFC (11271293).

BURKHOLDER-GUNDY-DAVIS INEQUALITY IN MARTINGALE HARDY SPACES WITH VARIABLE EXPONENT

Peide LIU, Maofa WANG

School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Received:2017-06-30 Revised:2017-12-07 Online:2018-08-25 Published:2018-08-25
Contact: Peide LIU,E-mail:pdliu@whu.edu.cn E-mail:pdliu@whu.edu.cn
Supported by:
The first author was supported by NSFC (11471251). The second author was supported by NSFC (11271293).

摘要/Abstract

摘要：

In this article, by extending classical Dellacherie's theorem on stochastic sequences to variable exponent spaces, we prove that the famous Burkholder-Gundy-Davis inequality holds for martingales in variable exponent Hardy spaces. We also obtain the variable exponent analogues of several martingale inequalities in classical theory, including convexity lemma, Chevalier's inequality and the equivalence of two kinds of martingale spaces with predictable control. Moreover, under the regular condition on σ-algebra sequence we prove the equivalence between five kinds of variable exponent martingale Hardy spaces.

关键词: variable exponent Lebesgue space, martingale inequality, Dellacherie theorem, Burkholder-Gundy-Davis inequality, Chevalier inequality

Abstract:

Key words: variable exponent Lebesgue space, martingale inequality, Dellacherie theorem, Burkholder-Gundy-Davis inequality, Chevalier inequality

刘培德, 王茂发. BURKHOLDER-GUNDY-DAVIS INEQUALITY IN MARTINGALE HARDY SPACES WITH VARIABLE EXPONENT[J]. 数学物理学报(英文版), 2018, 38(4): 1151-1162.

Peide LIU, Maofa WANG. BURKHOLDER-GUNDY-DAVIS INEQUALITY IN MARTINGALE HARDY SPACES WITH VARIABLE EXPONENT[J]. Acta mathematica scientia,Series B, 2018, 38(4): 1151-1162.

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BURKHOLDER-GUNDY-DAVIS INEQUALITY IN MARTINGALE HARDY SPACES WITH VARIABLE EXPONENT

BURKHOLDER-GUNDY-DAVIS INEQUALITY IN MARTINGALE HARDY SPACES WITH VARIABLE EXPONENT

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