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.
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 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).
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 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).
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
SN - 1867-1152
VL - 2
SP - 389
EP - 404
JO - Advances in Pure and Applied Mathematics
JF - Advances in Pure and Applied Mathematics
IS - 3-4
ER -