Monotonicity of generalized frequencies and the strong unique continuation property for fractional parabolic equations

We study the strong unique continuation property backwards in time for the nonlocal equation in Rn+1(0.1)(∂t−Δ)su=V(x,t)u,s∈(0,1). Our main result Theorem 1.2 can be thought of as the nonlocal counterpart of the result obtained in [30] for the case when s=1. In order to prove Theorem 1.2 we develop the regularity theory of the extension problem for the equation (0.1). With such theory in hands we establish: