Dual spaces and John-Nirenberg inequalities of martingale Hardy-Lorentz-Karamata spaces. (English) Zbl 1317.42021

Summary: In this paper, the generalized BMO martingale spaces are introduced as the dual spaces of martingale Hardy-Lorentz-Karamata spaces \(H_{p,q,b}^s\), which completes the very recent result [K.-P. Ho, Q. J. Math. 65, No. 3, 985–1009 (2014; Zbl 1341.42039)] in the case \(0< p\leq 1, 1< q< \infty\). Moreover, by duality we obtain a new John-Nirenberg theorem when the stochastic basis is regular.


42B35 Function spaces arising in harmonic analysis
42B30 \(H^p\)-spaces
60G42 Martingales with discrete parameter
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems


Zbl 1341.42039
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