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Atomic decomposition of a real Hardy space for Jacobi analysis

Atomic decomposition of a real Hardy space for Jacobi analysis Let (ℝℝ + , ΔΔ( x ) dx ) be a Jacobi hypergroup with weight function ΔΔ( x ) = c (sinh x ) 2 αα +1 (cosh x ) 2 ββ +1 . As in the Euclidean case, the real Hardy space H 1 (ΔΔ) for (ℝℝ + , ΔΔ( x ) dx ) is defined as the set of all locally integrable functions on ℝℝ + whose radial maximal functions belong to L 1 (ΔΔ). In this paper we give a characterization of H 1 (ΔΔ) in terms of weighted Triebel–Lizorkin spaces on ℝℝ via the Abel transform. As an application, we introduce three types of atoms for (ℝℝ + , ΔΔ), one of them is smooth, and give an atomic decomposition of H 1 (ΔΔ). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Pure and Applied Mathematics de Gruyter

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