## Abstract

Let L be a nonnegative self-adjoint operator on L^{2}(ℝ^{n}) satisfying the reinforced (pl,p'_{l}) off-diagonal estimates, where pl [1,2) and p'_{L} denotes its conjugate exponent. Assume that p (0,1] and the weight w satisfies the reverse Hölder inequality of order (p'_{L}/p)'. In particular, if the heat kernels of the semigroups {e~^{tL}}t>0 satisfy the Gaussian upper bounds, thenpL = 1 and hence w G A_{00}(ℝ^{n}). In this paper, the authors introduce the weighted Hardy spaces H^{p} _{L w}(ℝ^{n}) associated with the operator L, via the Lusin area function associated with the heat semigroup generated by L. Characterizations of H^{p} _{L w} (ℝ^{n}), in terms of the atom and the molecule, are obtained. As applications, the bounded-ness of singular integrals such as spectral multipliers, square functions and Riesz transforms on weighted Hardy spaces H_{L} ^{p} _{w}(ℝ^{n}) are investigated. Even for the Schrödinger operator - Δ + V with 0 < V e L1_{oc}(ℝ^{n}), the obtained results in this paper essentially improve the known results by extending the narrow range of the weights into the whole A∞(Rn) weights.

Original language | English |
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Pages (from-to) | 1127-1166 |

Number of pages | 40 |

Journal | Taiwanese Journal of Mathematics |

Volume | 17 |

Issue number | 4 |

DOIs | |

Publication status | Published - 23 Jul 2013 |