Abstract
In this paper we introduce the generalized BMO martingale spaces by stopping time sequences, which enable us to characterize the dual spaces of martingale Hardy-Lorentz spaces H s p,q for 0 < p ≤ 1,1 < q < ∞. Moreover, by duality we obtain a John-Nirenberg theorem for the generalized BMO martingale spaces when the stochastic basis is regular. We also extend the boundedness of fractional integrals to martingale Hardy-Lorentz spaces.
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