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arXiv · 2408.07248

Generalized square function estimates for curves and their conical extensions

Robert Schippa
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Abstract

We show sharp square function estimates for curves in the plane whose curvature degenerates at a point and estimates sharp up to endpoints for cones over these curves. To this end, for curves of finite type we extend the classical C\'ordoba--Fefferman biorthogonality. For cones over degenerate curves, we analyze wave envelope estimates proved via High-Low-decomposition. The arguments are subsequently extended to the cone over the complex parabola.

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Robert Schippa. 2024-08-14. Generalized square function estimates for curves and their conical extensions. https://arxiv.org/abs/2408.07248

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