Doob’s and Burkholder-Davis-Gundy inequalities with variable exponent,Proceedings of the American Mathematical Society

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Doob’s and Burkholder-Davis-Gundy inequalities with variable exponent
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-12-16 , DOI: 10.1090/proc/15262
Ferenc Weisz

Abstract:Let $p(\cdot )$ be a measurable function defined on a probability space $\Omega$ and $p_- \colonequals \inf _{x\in \Omega }p(x)$ , $p_+\colonequals \sup _{x\in \Omega }p(x)$ . Under a probabilistic version of the log-Hölder continuity of $1/p(\cdot )$ , Doob's inequality is proved if $1 \leq p_- \leq p_+<\infty$ .

中文翻译：

具有可变指数的Doob和Burkholder-Davis-Gundy不等式

摘要：设 $p（\ cdot）$ 是一个概率空间中定义的测函数 $\ Omega$ 和，。在log-Hölder连续性的概率形式下，Doob的不等式证明为。 $p_- \ colonequals \ inf _ {x \ in \ Omega} p（x）$ $p _ + \ colonequals \ sup _ {x \ in \ Omega} p（x）$ $1 / p（\ cdot）$ $1 \ leq p_- \ leq p _ + <\ infty$

更新日期：2021-01-11

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