On convergence properties for generalized Schrödinger operators along tangential curves

2021/11/17 by Wenjuan Li, Li, Wenjuan, Huiju Wang +1 · 2 citations
Mathematics · #35S10 #42B20 #42B25 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2111.09186

openalex publication_date 2021/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider convergence properties for generalized Schrödinger operators along tangential curves in ℝⁿ × ℝ with less smoothness comparing with Lipschitz condition. Firstly, we obtain sharp convergence rate for generalized Schrödinger operators with polynomial growth along tangential curves in ℝⁿ × ℝ, n ≥ 1. Secondly, it was open until now on pointwise convergence of solutions to the Schrödinger equation along non-C¹ curves in ℝⁿ × ℝ, n≥ 2, we obtain the corresponding results along some tangential curves when n=2 by the broad-narrow argument and polynomial partitioning. Moreover, the corresponding convergence rate will follow. Thirdly, we get the convergence result along a family of restricted tangential curves in ℝ × ℝ. As a consequence, we obtain the sharp L^p-Schrödinger maximal estimates along tangential curves in ℝ × ℝ.

Citations

• A note on pointwise convergence for the Schrödinger equation

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• Sharp convergence rate of Schrödinger operator along curves
• On the rate of convergence for Landau type Schrödinger Operators

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