TY - JOUR

T1 - Atomic decomposition of a real Hardy space for Jacobi analysis

AU - Kawazoe, Takeshi

N1 - Funding Information:
The author was supported by Grant-in-Aid for Scientific Research (C), No. 20540188, Japan Society for the Promotion of Science.
Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.

PY - 2011/9

Y1 - 2011/9

N2 - 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 H 1(Δ) for (ℝ +; Δ(x)dx) is defined as the set of all locally integrable functions on ℝ + whose radial maximal functions belong to L 1(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 H 1(Δ).

AB - 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 H 1(Δ) for (ℝ +; Δ(x)dx) is defined as the set of all locally integrable functions on ℝ + whose radial maximal functions belong to L 1(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 H 1(Δ).

KW - Atomic decomposition

KW - Hardy space

KW - Jacobi analysis

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U2 - 10.1515/APAM.2010.036

DO - 10.1515/APAM.2010.036

M3 - Article

AN - SCOPUS:84858394238

VL - 2

SP - 389

EP - 404

JO - Advances in Pure and Applied Mathematics

JF - Advances in Pure and Applied Mathematics

SN - 1867-1152

IS - 3-4

ER -