  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 $H_{p,q}^s$ for $0<p\leq1, 1<q<\infty$. 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.
