New variable martingale Hardy spaces

This is the authors' abstract. We don't add key points for this paper.

We investigate various variable martingale Hardy spaces corresponding to variable Lebesgue spaces Lp(· ) defined by rearrangement functions. In particular, we show that the dual of martingale variable Hardy space Hp(· )ˢ with 0<p₋≤ p₊≤ 1 can be described as a BMO-type space and establish martingale inequalities among these martingale Hardy spaces. Furthermore, we give an application of martingale inequalities in stochastic integral with Brownian motion.