### 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 language | English |
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Pages (from-to) | 389-404 |

Number of pages | 16 |

Journal | Advances in Pure and Applied Mathematics |

Volume | 2 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - 2011 Sep 1 |

### Keywords

- Atomic decomposition
- Hardy space
- Jacobi analysis

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Kawazoe, T. (2011). Atomic decomposition of a real Hardy space for Jacobi analysis.

*Advances in Pure and Applied Mathematics*,*2*(3-4), 389-404. https://doi.org/10.1515/APAM.2010.036