DOOB’S MAXIMAL INEQUALITIES FOR MARTINGALES IN VARIABLE LEBESGUE SPACE  

作　　者：Peide LIU 刘培德(School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China)

机构地区：[1]School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China

出　　处：《Acta Mathematica Scientia》2021年第1期283-296,共14页数学物理学报（B辑英文版）

基　　金：supported by the NSFC(11471251)。

摘　　要：In this paper we deal with the martingales in variable Lebesgue space over a probability space.We first prove several basic inequalities for conditional expectation operators and give several norm convergence conditions for martingales in variable Lebesgue space.The main aim of this paper is to investigate the boundedness of weak-type and strong-type Doob’s maximal operators in martingale Lebesgue space with a variable exponent.In particular,we present two kinds of weak-type Doob’s maximal inequalities and some necessary and sufficient conditions for strong-type Doob’s maximal inequalities.Finally,we provide two counterexamples to show that the strong-type inequality does not hold in general variable Lebesgue spaces with p>1.

关 键 词：variable Lebesgue space martingale inequality norm convergence Doob’s maximal inequality 

分 类 号：O178[理学—数学]