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arXiv · 2403.04721

A sharp H\"{o}rmander condition for bilinear Fourier multipliers with Lipschitz singularities

Jiao Chen·Martin Hsu·Fred Yu-Hsiang Lin
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Abstract

This paper studies the $L^{p}$ boundedness of bilinear Fourier multipliers in the local $L^{2}$ range. We assume a H\"{o}rmander condition relative to a singular set that is a finite union of Lipschitz curves. The H\"{o}rmander condition is sharp with respect to the Sobolev exponent. Our setup generalizes the non-degenerate bilinear Hilbert transform but avoids issues of uniform bounds near degeneracy.

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Jiao Chen, Martin Hsu, Fred Yu-Hsiang Lin. 2024-03-07. A sharp H\"{o}rmander condition for bilinear Fourier multipliers with Lipschitz singularities. https://arxiv.org/abs/2403.04721

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