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

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

Acta mathematica scientia,Series B ›› 2018, Vol. 38 ›› Issue (4): 1151-1162.doi: 10.1016/S0252-9602(18)30805-1

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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).

Abstract

Abstract:

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.

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

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

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