Imaginary powers of Laplace operators

Abstract

We show that if L is a second-order uniformly elliptic operator in divergence form on Rd, then C1(1+|a|)d/2 < \\Lia\\Li→L1,∞ ≥ C2(1+|a|)d/2. We also prove that the upper bounds remain true for any operator with the finite speed propagation property.