## Abstract

Let X be a space of homogeneous type. Assume that an operator L has a bounded holomorphic functional calculus on L^{2}(X) and the kernel of the heat semigroup {e-tL}t>0 satisfies the Davies-Gaffney estimates. Without the assumption that L is self-adjoint, we develop a theory of Hardy spaces HLp(X), 0<p≤1, which includes a molecular decomposition, an atomic decomposition, a square function characterization, duality of Hardy and Lipschitz spaces, and a Marcinkiewicz type interpolation theorem. As applications, we show that L has a bounded holomorphic functional calculus on HLp(X) for all p>0 and certain Riesz transforms associated to L are bounded from HLp(X) to L^{p}(X) for all 0<p≤2.

Original language | English |
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Pages (from-to) | 1409-1437 |

Number of pages | 29 |

Journal | Journal of Functional Analysis |

Volume | 264 |

Issue number | 6 |

DOIs | |

Publication status | Published - 15 Mar 2013 |