New bounds for Stein's square functions in higher dimensions

2021/08/26 by Shengwen Gan, Gan, Shengwen, Changkeun Oh +3
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Approximation and Integration #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2108.11567

openalex publication_date 2021/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We improve the L^p(ℝⁿ) bounds on Stein's square function to the best-known range of the Fourier restriction problem when n≥4. Applications including certain local smoothing estimates are also discussed.

Citations

• On the multilinear restriction and Kakeya conjectures
• Improved bounds for the Kakeya maximal conjecture in higher dimensions
• On the Bochner-Riesz operator in ℝ³
• A note on Fourier restriction and nested Polynomial Wolff axioms

Related

• New bounds for Stein's square function in ℝ³
• L^p--boundedness of Stein's square functions associated to Fourier--Bessel expansions
• L² restriction estimates from the Fourier spectrum
• Improved Stein inequalities for the Fourier transform
• Some inequalities for the Fourier transform and their limiting behaviour