The John–Nirenberg inequality for Orlicz–Lorentz spaces in a probabilistic setting
DOI:
https://doi.org/10.33044/revuma.3106Abstract
The John–Nirenberg inequality is widely studied in the field of mathematical analysis and probability theory. In this paper we study a new type of the John–Nirenberg inequality for Orlicz–Lorentz spaces in a probabilistic setting. To be precise, let $0 < q \leq \infty$ and $\Phi$ be an $N$-function with some proper restrictions. We prove that if the stochastic basis $\{\mathcal{F}_n\}_{n \geq 0}$ is regular, then $BMO_{\Phi,q}=BMO$, with equivalent (quasi)-norms. The result is new, which improves previous work on martingale Hardy theory.
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