Dual Spaces And John–Nirenberg Inequalities of Martingale Hardy–Lorentz–Karamata Spaces

jiao, yong; xie, guangheng; zhou, dejian;

In this paper, the generalized BMO martingale spaces are introduced as the dual spaces of martingale Hardy–Lorentz–Karamata spaces Hs
p,q,b, which completes the very recent result [Quart. J. Math. 65 (2014), 985–1009] in the case 0 < p ≤ 1, 1 < q < ∞. Moreover, by duality we obtain a
new John–Nirenberg theorem when the stochastic basis is regular.