Quantitative uniqueness for fractional heat type operators

Abstract

In this paper we obtain quantitative bounds on the maximal order of vanishing for solutions to $(\partial_t - \Delta)^s u =Vu$ for $s\in [1/2, 1)$ via new Carleman estimates. Our main result Theorem 1.1 and Theorem 1.3 can be thought of as a parabolic generalization of the corresponding quantitative uniqueness result in the time independent case due to R\"uland and it can also be regarded as a nonlocal generalization of a similar result due to Zhu for solutions to local parabolic equations.