Uniform Sobolev estimates in ℝⁿ involving singular potentials

2021/01/24 by Xiaoqi Huang, Christopher D. Sogge, Huang, Xiaoqi +1
Mathematics · #35 #58 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2101.09826

openalex publication_date 2021/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize the Stein-Tomas [17] L²-restricition theorem and the uniform Sobolev estimates of Kenig, Ruiz and the second author [11] by allowing critically singular potential. We also obtain Strichartz estimates for Schrödinger and wave operators with such potentials. Due to the fact that there may be nontrivial eigenfunctions we are required to make certain spectral assumptions, such as assuming that the solutions only involve sufficiently large frequencies.

Citations

• Spectral properties of Schrödinger operators and time-decay of the wave functions
• Decay estimates for Schrödinger operators

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