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Atomic decomposition of a real Hardy space for Jacobi analysis
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Takeshi Kawazoe
Published/Copyright:
September 17, 2010
Abstract
Let (ℝ+, Δ(x)dx) be a Jacobi hypergroup with weight function Δ(x) = c(sinh x)2α+1(cosh x)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 H1(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).
Received: 2010-04-29
Accepted: 2010-05-31
Published Online: 2010-09-17
Published in Print: 2011-September
© de Gruyter 2011
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Articles in the same Issue
- Geometric and harmonic analysis on homogeneous spaces
- On the multiplicity formula of compact nilmanifolds with flat orbits
- Hilbert transform and related topics associated with Jacobi–Dunkl operators of compact and noncompact types
- Atomic decomposition of a real Hardy space for Jacobi analysis
- Unitary holomorphic multiplier representations over a homogeneous bounded domain
- A deformation approach of the Kirillov map for exponential groups
- Visible actions on the non-symmetric homogeneous space SO(8, ℂ)/G2(ℂ)
- A Paley–Wiener theorem for some eigenfunction expansions
- Estimate of the Lp-Fourier transform norm for connected nilpotent Lie groups
