Atomic decomposition of a real Hardy space for Jacobi analysis

Takeshi Kawazoe

Research output: Contribution to journalArticle

Abstract

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).

Original languageEnglish
Pages (from-to)389-404
Number of pages16
JournalAdvances in Pure and Applied Mathematics
Volume2
Issue number3-4
DOIs
Publication statusPublished - 2011 Sep 1

Keywords

  • Atomic decomposition
  • Hardy space
  • Jacobi analysis

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Atomic decomposition of a real Hardy space for Jacobi analysis'. Together they form a unique fingerprint.

  • Cite this