Sharp convergence for sequences of Schrödinger means and related generalizations

Abstract

For decreasing sequences $\{t_n{\}}_{n=1}^{\infty }$ converging to zero, we obtain the almost everywhere convergence results for sequences of Schrödinger means $e^{i{t}_n\Delta }f$, where $f\in H^s({\mathbb{R}}^N),N\ge 2$. The convergence results are sharp up to the endpoints, and the method can also be applied to get the convergence results for the fractional Schrödinger means and nonelliptic Schrödinger means.

References in corpus (1)

• A note on pointwise convergence for the Schrödinger equation

Cited by in corpus (1)

• Bourgain's counterexample in the sequential convergence problem for the Schrödinger equation