Weighted L^p estimates for powers of selfadjoint operators

We prove Lp and weighted Lp estimates for bounded functions of a selfadjoint operator satisfying a pointwise Gaussian estimate for its heat kernel. As an application, we obtain weighted estimates for fractional powers of an electromagnetic Schrödinger operator with singular coefficients. The proofs are based on a modification of techniques due to Hebisch (1990) [17] and Auscher and Martell (2006) [4].