Characterizations of Hardy spaces associated with Laplace–Bessel operators

Abstract

In this paper, we obtain a characterization of $$H^{p}_{\varDelta _{\nu }}({\mathbb {R}}^{n}_{+})$$ Hardy spaces by using atoms associated with the radial maximal function, the nontangential maximal function and the grand maximal function related to $$\varDelta _{\nu }$$ Laplace–Bessel operator for $$\nu >0$$ and $$1<p<\infty $$. As an application, we further establish an atomic characterization of Hardy spaces $$H^{p}_{\varDelta _{\nu }}({\mathbb {R}}^{n}_{+})$$ in terms of the high order Riesz–Bessel transform for $$0<p\le 1$$.