Square function estimates for cones over quadratic manifolds

2025/02/18 by Robert Schippa, Schippa, Robert · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2502.13275

openalex publication_date 2025/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the L⁴-square function estimates for the parabola and the half-cone to quadratic manifolds in higher dimensions and their conical extensions. To this end, we require transversality for the tangent spaces of the quadratic manifolds at separated points. This allows us to show biorthogonality for the associated system of quadratic equations. For the conical extensions we obtain a wave envelope estimate by High-Low arguments.

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