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Dual spaces of multi-parameter martingale Hardy spaces. (English) Zbl 1334.42049

Summary: In this paper, we introduce the generalized multi-parameter martingale \(\text{BMO}\) spaces. The atomic decomposition of the multi-parameter martingale Hardy-Lorentz space \(H_{p,q}^s\) is given. With the help of this, the dual space of \(H_{p,q}^s\) is characterized as the generalized \(\text{BMO}\) space. Finally, as an application, the John-Nirenberg inequality is generalized for multi-parameters.

MSC:

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