A Note on Almost Everywhere Convergence Along Tangential Curves to the Schr\"odinger Equation Initial Datum

In this short note, we give an easy proof of the following result: for n≥ 2, t→0lim \,eitΔf(x+γ(t)) = f(x) almost everywhere whenever γ is an α-H\"older curve with 12≤ α≤ 1 and f∈ Hˢ(Rⁿ), with s > n/2(n+1). This is the optimal range of regularity up to the endpoint.