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Yang, Dachun; Yang, Dongyong

Real-variable characterizations of Hardy spaces associated with Bessel operators. (English) Zbl 1227.42021

Anal. Appl., Singap. 9, No. 3, 345-368 (2011).
The authors prove characterizations of the atomic Hardy spaces \(H^p((0,\infty),dm_\lambda)\) associated with the Bessel operator \(\Delta_\lambda = -\frac{d^2}{dx^2}-\frac{2\lambda}x\frac d{dx} \), where \(dm_\lambda(x)=x^{2\lambda}dx\), \(p\in ((2\lambda+1)/(2\lambda+2),1]\) and \(\lambda\in(0,\infty)\). 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)].
Reviewer: Krzysztof Stempak (Wrocław)

Cited in 26 Documents

MSC:

42B30 \(H^p\)-spaces
42B25 Maximal functions, Littlewood-Paley theory
42B35 Function spaces arising in harmonic analysis

Keywords:

Hardy space; Bessel operator; maximal function; Riesz transform; Littlewood-Paley \(g\)-function; Lusin-area function

Citations:

Zbl 1179.42016; Zbl 1193.46018
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