Domains of dependence for subelliptic wave equations and unique continuation for fractional powers of Hörmander's operators

We prove the sharp domain of dependence property for solutions to subelliptic wave equations for sums of squares of vector fields satisfying Hörmander bracket condition. We deduce a unique continuation property for the square root of subelliptic Laplace operators under an additional analyticity condition. Then, with a different, more involved method, we prove the same result of unique continuation for more general $s$-powers ($0<s<1$).