Riesz transforms associated with higher-order Schrödinger type operators

2016/03/27 by Qingquan Deng, Yong Ding, Deng, Qingquan +3
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1603.08171

openalex publication_date 2016/03/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/02

Abstract

In this paper, let L=L₀+V be a Schrödinger type operator where L₀ is higher order elliptic operator with complex coefficients in divergence form and V is signed measurable function, under the strongly subcritical assumption on V, the authors study the L^q boundedness of Riesz transforms ∇^mL^-1/2 for q≤ 2 and obtain a sharp result. Furthermore, the authors impose extra regularity assumptions on V to obtain the L^q boundedness of Riesz transforms ∇^mL^-1/2 for q>2. As an application, the main results can be applied to the operator L=(-Δ)^m-γ|x|^-2m for suitable γ

Citations

• Strichartz estimates for the Wave and Schrodinger Equations with the Inverse-Square Potential

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