We investigate various variable martingale Hardy spaces corresponding to variable Lebesgue spaces $\mathcal {L}_{p(\cdot )}$ defined by rearrangement functions. In particular, we show that the dual of martingale variable Hardy space $\mathcal {H}_{p(\cdot )}^{s}$ with $0<p_{-}\leq p_{+}\leq 1$ 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.

中文翻译：

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新的变量鞅哈代空间

我们研究了与由重排函数定义的变量 Lebesgue 空间$\mathcal {L}_{p(\cdot )}$相对应的各种变量鞅哈代空间。特别是，我们证明了鞅变量 Hardy 空间$\mathcal {H}_{p(\cdot )}^{s}$与$0<p_{-}\leq p_{+}\leq 1$的对偶可以被描述为 BMO 型空间，并在这些鞅 Hardy 空间之间建立鞅不等式。此外，我们给出了鞅不等式在布朗运动随机积分中的应用。