L^p boundedness of wave operators for higher order schrödinger operators with threshold eigenvalues

2025/06/19 by M. Burak Erdogan, William R. Green, Erdogan, M. Burak +3 · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics #math.AP #math.SP

paper · pdf · doi:10.48550/arxiv.2506.16378

openalex publication_date 2025/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the higher order Schrödinger operator H=(-Δ)^m+V(x) in n dimensions with real-valued potential V when n>2m, m∈ \mathbb N when H has a threshold eigenvalue. We adapt our recent results for m≥ 1 when n>4m to lower dimensions 2m2m. The range is p∈ [1,∞) and p∈[1,∞] when k₀=2m and k₀>2m respectively. The proofs apply in the classical m=1 case as well and streamlines existing arguments in the eigenvalue only case, in particular the L^∞(\mathbb Rⁿ) boundedness is new when n>3.

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