Weisz, Ferenc Dual spaces of multi-parameter martingale Hardy spaces. (English) Zbl 1334.42049 Q. J. Math. 67, No. 1, 137-145 (2016). 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. Cited in 15 Documents 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 Keywords:multi-parameter martingale Hardy-Lorentz spaces; generalized BMO spaces; atomic decomposition; John-Nirenberg inequality PDFBibTeX XMLCite \textit{F. Weisz}, Q. J. Math. 67, No. 1, 137--145 (2016; Zbl 1334.42049) Full Text: DOI Link