Generalized square function estimates for curves and their conical extensions
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 Córdoba--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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.07248
- arXiv:
- arXiv:2408.07248
- Bibcode:
- 2024arXiv240807248S
- Keywords:
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- Mathematics - Classical Analysis and ODEs
- E-Print:
- 28 pages, 3 figures