### Abstract

Let X be a space of homogeneous type, and L be the generator of a semigroup with Gaussian kernel bounds on L^{2}(X). We define the Hardy spaces H_{s}
^{p}(X) of X for a range of p, by means of area integral function associated with the Poisson semigroup of L, which is proved to coincide with the usual atomic Hardy spaces H_{at}
^{p}(X) on spaces of homogeneous type.

Original language | English |
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Pages (from-to) | 3181-3189 |

Number of pages | 9 |

Journal | Proceedings of the American Mathematical Society |

Volume | 131 |

Issue number | 10 |

DOIs | |

Publication status | Published - Oct 2003 |

### Keywords

- Atomic decomposition
- Calderón-type reproducing formula
- Hardy spaces
- Semigroup
- Spaces of homogeneous type

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## Cite this

Duong, X. T., & Yan, L. (2003). Hardy spaces of spaces of homogeneous type.

*Proceedings of the American Mathematical Society*,*131*(10), 3181-3189. https://doi.org/10.1090/S0002-9939-03-06868-0