March 7, 2024Open Access

A sharp H\"ormander condition for bilinear Fourier multipliers with Lipschitz singularities

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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\"ormander condition relative to a singular set that is a finite union of Lipschitz curves. The H\"ormander 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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Chen et al. (Thu,) studied this question.

synapsesocial.com/papers/68e7567db6db6435876cde6c https://doi.org/https://doi.org/10.48550/arxiv.2403.04721

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