A Note on Non-tangential Convergence for Schrödinger Operators

Abstract

The goal of this note is to establish non-tangential convergence results for Schrödinger 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 a upper bound for $p$ such that the Schrödinger maximal function is bounded from $H^s({\mathbb{R}}^n)$ to $L^p({\mathbb{R}}^n)$ for any $s>\frac{n}{2(n+1)}$.

References in corpus (1)

• Pointwise convergence along restricted directions for the fractional Schrödinger equation