Negative Order Bochner-Riesz Operators for the Critical Magnetic Schrödinger Operator in ℝ²

2025/10/05 by Guo, Huanqing, Junyong Zhang, Jiqiang Zheng +2
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2510.04082

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

Abstract

This paper studies the sharp L^p-L^q boundedness of the Bochner-Riesz operator S^δ_λ(L_A) associated with a scaling-critical magnetic Schrödinger operator L_A on ℝ², where δ∈ (-3/2, 0). We determine the conditions on the exponents p and q under which the operator is bounded from L^p(ℝ²) to L^q(ℝ²). Our main result characterizes the boundedness region as a pentagonal subset Δ(δ) of the (1/p, 1/q)-plane, extending previous uniform resolvent result in Fanelli, Zhang and Zheng[Int. Math. Res. Not., 20(2023), 17656-17703].

Citations

• Intertwining operators beyond the Stark Effect
• Bochner-Riesz means for critical magnetic Schrödinger operators in \mathbb R²
• Endpoint eigenfunction bounds for the Hermite operator
• Uniform resolvent estimates for critical magnetic Schrödinger operators in 2D
• The Bochner-Riesz problem: an old approach revisited
• Bochner-Riesz means for the Hermite and special Hermite expansions
• L^p-bounds on spectral clusters associated to polygonal domains
• Bounds on oscillatory integral operators based on multilinear estimates

Related

• Bochner-Riesz means for critical magnetic Schrödinger operators in \mathbb R²
• Uniform resolvent estimates for critical magnetic Schrödinger operators in 2D
• Maximal Inequalities and Riesz Transform Estimates on L^p Spaces for Magnetic Schrodinger Operators II
• Maximal Inequalities and Riesz Transform Estimates on L^p Spaces for Magnetic Schrodinger Operators I
• L^p-estimates for the wave equation with critical magnetic field in higher dimensions