A Note on Non-tangential Convergence for Schrödinger Operators

The goal of this note is to establish non-tangential convergence results for Schrodinger operators along restricted curves. We consider the relationship between the dimension of this kind of approach region and the regularity for the initial data which implies convergence. As a consequence, we obtain an upper bound for p such that the Schrodinger maximal function is bounded from $$H^{s}(\mathbb {R}^{n})$$ to $$L^{p}(\mathbb {R}^{n})$$ for any $$s > \frac{n}{2(n+1)}$$ .