A sharp Schrodinger maximal estimate in ${\mathbb{R}}^2$

Abstract

We show that ${\lim }_{t\to 0}{e}^{it\Delta }f(x)=f(x)$ almost everywhere for all $f\in H^s({\mathbb{R}}^2)$ provided that $s>1/3$. This result is sharp up to the endpoint. The proof uses polynomial partitioning and decoupling.

arXiv comment29 pages, 4 figures, accepted for publication in the Annals of Math

References in corpus (2)

• Schrödinger maximal function estimates via the pseudoconformal transformation
• An improved necessary condition for the Schrödinger maximal estimate

Cited by in corpus (2)

• A note on pointwise convergence for the Schrödinger equation
• Transference of local to global $L^2$ maximal estimates for dispersive partial differential equations