The predual and John-Nirenberg inequalities on generalized BMO martingale spaces

Jiao, Yong; Wu, Lian; Yang, Anming; Yi, Rui

doi:10.1090/tran/6657

The predual and John-Nirenberg inequalities on generalized BMO martingale spaces
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by Yong Jiao, Lian Wu, Anming Yang and Rui Yi PDF

Trans. Amer. Math. Soc. 369 (2017), 537-553 Request permission

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

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