The paper is mainly devoted to establishing an extension of the John–Nirenberg theorem for martingales. More precisely, let 1 < p < ∞ and 0 < q < ∞. If the stochastic basis (Fn)n≥0 is regular, then BMOp,q = BMO1 with the equivalent norms. Our method is to use a new atomic decomposition construction of the martingale Hardy space.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, No. 11, pp. 1571–1577, November, 2018.
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Li, L. A Remark on John–Nirenberg Theorem for Martingales. Ukr Math J 70, 1812–1820 (2019). https://doi.org/10.1007/s11253-019-01609-8
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DOI: https://doi.org/10.1007/s11253-019-01609-8