Atomic decomposition of a real Hardy space for Jacobi analysis

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

Fingerprint

Atomic Decomposition
Triebel-Lizorkin Space
Hypergroup
Maximal Function
Weighted Spaces
Hardy Space
Radial Functions
Jacobi
Weight Function
Euclidean
Transform

Keywords

  • Atomic decomposition
  • Hardy space
  • Jacobi analysis

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Atomic decomposition of a real Hardy space for Jacobi analysis. / Kawazoe, Takeshi.

In: Advances in Pure and Applied Mathematics, Vol. 2, No. 3-4, 09.2011, p. 389-404.

Research output: Contribution to journalArticle

@article{46e01d82d89b474593193fd03e4f4f7a,
title = "Atomic decomposition of a real Hardy space for Jacobi analysis",
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).",
keywords = "Atomic decomposition, Hardy space, Jacobi analysis",
author = "Takeshi Kawazoe",
year = "2011",
month = "9",
doi = "10.1515/APAM.2010.036",
language = "English",
volume = "2",
pages = "389--404",
journal = "Advances in Pure and Applied Mathematics",
issn = "1867-1152",
publisher = "Walter de Gruyter GmbH & Co. KG",
number = "3-4",

}

TY - JOUR

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

AU - Kawazoe, Takeshi

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

UR - http://www.scopus.com/inward/record.url?scp=84858394238&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84858394238&partnerID=8YFLogxK

U2 - 10.1515/APAM.2010.036

DO - 10.1515/APAM.2010.036

M3 - Article

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 -