Real-Variable Characterizations Of Hardy Spaces Associated With Bessel Operators

Details Real-Variable Characterizations Of Hardy Spaces Associated With Bessel Operators Real-Variable Characterizations Of Hardy Spaces Associated With Bessel Operators

2011-02-07

arxiv.org/abs/1102.1217v1

Mathematics

Classical Analysis and ODEs

Anal. Appl. (Singap.) (to appear)

Scientific paper

Let $\lambda>0$, $p\in((2\lz+1)/(2\lz+2), 1]$, and $\triangle_\lambda\equiv-\frac{d^2}{dx^2}-\frac{2\lambda}{x} \frac d{dx}$ be the Bessel operator. In this paper, the authors establish the characterizations of atomic Hardy spaces $H^p((0, \infty), dm_\lambda)$ associated with $\triangle_\lambda$ 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, where $dm_\lambda(x)\equiv x^{2\lambda}\,dx$. As an application, the authors further obtain the Riesz transform characterization of these Hardy spaces.

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