## Abstract

Let script X sign be a space of homogeneous type. Assume that L has a bounded holomorphic functional calculus on L
^{2}(Ω) and L generates a semigroup with suitable upper bounds on its heat kernels where Ω is a measurable subset of script X sign. For appropriate bounded holomorphic functions b, we can define the operators b(L) on L
^{p}(Ω), 1 ≤ p ≤ ∞. We establish conditions on positive weight functions u, v such that for each p, l < p < ∞, there exists a constant c
_{p} such that ∫
_{Ω}|b(L)f(x) |
^{p}u(x)dμ(x) ≤ c
_{p}||b||
_{∞}
^{p} ∫
_{Ω} |f(x)|
^{p}v(x)dμ(x) for all f ∈ L
^{P}(vdμ). Applications include two-weight L
^{p} inequalities for Schrödinger operators with non-negative potentials on R
^{n} and divergence form operators on irregular domains of R
^{n}.

Original language | English |
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Pages (from-to) | 1129-1152 |

Number of pages | 24 |

Journal | Journal of the Mathematical Society of Japan |

Volume | 57 |

Issue number | 4 |

DOIs | |

Publication status | Published - Oct 2005 |