Burkholder-Gundy-Davis Inequality in Martingale Hardy Spaces with   Variable Exponent
  In this paper, the classical Dellacherie's theorem about stochastic process is extended to variable exponent Lebesgue spaces. As its applications, we obtain variable exponent analogues of several famous inequalities in classical martingale theory, including convexity lemma, Burkholder-Gundy-Davis' inequality and Chevalier's inequality. Moreover, we investigate some other equivalent relations between variable exponent martingale Hardy spaces. 
Peide Liu, Maofa Wang
math.FA math.PR