## Abstract

In this paper, we establish suffcient conditions for a singular integral T to be bounded from certain Hardy spaces H^{p} _{L} to Lebesgue spaces L^{p}, 0 < p (≤ 1, and for the commutator of T and a BMO function to be weak-type bounded on Hardy space H(^{1} _{L}. We then show that our suffcient conditions are applicable to the following cases: (i) T is the Riesz transform or a square function associated with the Laplace- Beltrami operator on a doubling Riemannian manifold, (ii) T is the Riesz transform associated with the magnetic Schrödinger operator on a Euclidean space, and (iii) T = g(L) is a singular integral operator deffned from the holomorphic functional calculus of an operator L or the spectral multiplier of a non-negative self-adjoint operator L.

Original language | English |
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Pages (from-to) | 459-494 |

Number of pages | 36 |

Journal | Advances in Differential Equations |

Volume | 18 |

Issue number | 5-6 |

Publication status | Published - 2013 |