Resolvent Estimates for Schrödinger Operators with Potentials in Lebesgue Spaces

2020/04/22 by Tianyi Ren, Ren, Tianyi
Mathematics · #42B15 #42B35 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2004.10419

openalex publication_date 2020/04/22 · openalex created_date 2020/05/01 · openalex updated_date 2026/07/28

Abstract

We prove resolvent estimates in the Euclidean setting for Schrödinger operators with potentials in Lebesgue spaces: -Δ+V. The (L², L^p) estimates were already obtained by Blair-Sire-Sogge, but we extend their result to other (L^p, L^q) estimates using their idea and the result and method of Kwon-Lee on non-uniform resolvent estimates in the Euclidean space.

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