Sharp constants for John-Nirenberg and Reverse Hölder inequalities are the same on the circle, the interval, and the line, proved via a new martingale-based transference principle.
Klemes, A mean oscillation inequality , Proceedings of the American Mathematical Society 93:3 (1985), 497–500
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Sharp transference principle for $\mathrm{BMO}$ and $A_p$
Sharp constants for John-Nirenberg and Reverse Hölder inequalities are the same on the circle, the interval, and the line, proved via a new martingale-based transference principle.