Pointwise Convergence for sequences of Schrödinger means in ℝ²

2020/10/17 by Wenjuan Li, Li, Wenjuan, Huiju Wang +3
Mathematics · #35S10 #42B20 #42B25 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2010.08701

openalex publication_date 2020/10/17 · openalex created_date 2020/10/22 · openalex updated_date 2026/07/28

Abstract

We consider pointwise convergence of Schrödinger means e^it_nΔf(x) for f ∈ H^s(ℝ²) and decreasing sequences \t_n\_n=1^∞ converging to zero. The main theorem improves the previous results of [Sjölin, JFAA, 2018] and [Sjölin-Strömberg, JMAA, 2020] in ℝ². This study is based on investigating properties of Schrödinger type maximal functions related to hypersurfaces with vanishing Gaussian curvature.

Related

• Sharp convergence for sequences of nonelliptic Schrödinger means
• Pointwise convergence of sequential Schrödinger means
• Pointwise convergence of solutions to Schrödinger equations
• Schrödinger means in higher dimensions
• Convergence of sequences of Schrödinger means