A sharp Schrodinger maximal estimate in ℝ²

2016/12/28 by Du, Xiumin, Guth, Larry, Li, Xiaochun
#42B15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1612.08946

Abstract

We show that lim_{t → 0} e^itΔf(x) = f(x) almost everywhere for all f ∈ H^s (ℝ²) provided that s>1/3. This result is sharp up to the endpoint. The proof uses polynomial partitioning and decoupling.

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