A remark on Strichartz estimates for Schrödinger equations with slowly decaying potentials

2022/01/05 by Kouichi Taira · 4 citations
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Applied mathematics #Dimension (graph theory) #Generalization #Mathematical analysis #Mathematical physics #Mathematics #Pure mathematics #Schrödinger equation #Schrödinger's cat #Smoothing #Spectral Theory in Mathematical Physics #Statistics

paper · doi:10.1090/proc/15954

published in Proceedings of the American Mathematical Society 150(9), 3953-3958 (American Mathematical Society)

openalex publication_date 2022/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this short note, we prove Strichartz estimates for Schrödinger operators with slowly decaying singular potentials in dimension two. This is a generalization of the recent results by Mizutani, which are stated for dimension greater than two. The main ingredient of the proof is a variant of Kato’s smoothing estimate with a singular weight.

Citations

• Time decay for solutions of Schr�dinger equations with rough and time-dependent potentials

Cited by

• Strichartz estimates in Wiener amalgam spaces for Schrödinger equations with at most quadratic potentials
• Low-energy resolvent estimates for slowly decaying attractive potentials

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