Functional calculi of second-order elliptic partial differential operators with bounded measurable coefficients

Consider a second-order elliptic partial differential operator L in divergence form with real, symmetric, bounded measurable coefficients, under Dirichlet or Neumann conditions on the boundary of a strongly Lipschitz domain Omega. Suppose that 1 < p < infinity and mu > 0. Then L has a bounded H-infinity functional calculus in L-p(Omega), in the sense that \\f(L + cI)u\\(p) less than or equal to C sup(\arg lambda\<mu)\f(lambda)\\\u\\(p) for some constants c and C, and all bounded holomorphic functions f on the sector \arg lambda\ < mu that contains the spectrum of L + cI. We prove this by showing that the operators f(L + cI) are Calderon-Zygmund singular integral operators.