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) | pu(x)dμ(x) ≤ c p||b|| ∞ p ∫ Ω |f(x)| pv(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.