Let (ℝ+; Δ(x)dx) be a Jacobi hypergroup with weight function Δ(x) = c(sinhx)2α+1.coshx)2β+1. As in the Euclidean case, the real Hardy space H1(Δ) for (ℝ+; Δ(x)dx) is defined as the set of all locally integrable functions on ℝ+ whose radial maximal functions belong to L1(Δ). In this paper we give a characterization of H 1(Δ) in terms of weighted Triebel-Lizorkin spaces on ℝ via the Abel transform. As an application, we introduce three types of atoms for (ℝ+; Δ), one of them is smooth, and give an atomic decomposition of H1(Δ).
ASJC Scopus subject areas
- 数学 (全般)