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Real-variable characterizations of Hardy spaces associated with Bessel operators. (English) Zbl 1227.42021
The authors prove characterizations of the atomic Hardy spaces ${H}^{p}\left(\left(0,\infty \right),d{m}_{\lambda }\right)$ associated with the Bessel operator ${{\Delta }}_{\lambda }=-\frac{{d}^{2}}{d{x}^{2}}-\frac{2\lambda }{x}\frac{d}{dx}$, where $d{m}_{\lambda }\left(x\right)={x}^{2\lambda }dx$, $p\in \left(\left(2\lambda +1\right)\left(2\lambda +2\right),1\right]$ and $\lambda \in \left(0,\infty \right)$. The characterizations are given in terms of the radial maximal function, the nontangential maximal function, the grand maximal function, the Littlewood-Paley $g$-function and the Lusin area function. Arguments in the proofs are partially based on results and notions introduced by Y.-S. Han, D. Müller and D.-C. Yang in [Math. Nachr. 279, No. 13–14, 1505–1537 (2006; Zbl 1179.42016)] and [Abstr. Appl. Anal. 2008, Article ID 893409 (2008; Zbl 1193.46018)].
##### MSC:
 42B30 ${H}^{p}$-spaces (Fourier analysis) 42B25 Maximal functions, Littlewood-Paley theory 42B35 Function spaces arising in harmonic analysis