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rearrangement function

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

New variable martingale Hardy spaces
Part of
- Stochastic processes
Yong Jiao, Dan Zeng, Dejian Zhou
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 152 / Issue 2 / April 2022

Published online by Cambridge University Press:

23 April 2021, pp. 450-478

Print publication:

April 2022
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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.