REAL-VARIABLE CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BESSEL OPERATORS

Abstract

Let λ > 0, p ∈ ((2λ + 1)/(2λ + 2), 1], and [Formula: see text] be the Bessel operator. In this paper, the authors establish the characterizations of atomic Hardy spaces H p ((0,∞),dm λ ) associated with △ λ 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 λ (x) ≡ x 2λ dx. As an application, the authors further obtain the Riesz transform characterization of these Hardy spaces.