A sharp Hörmander condition for bilinear Fourier multipliers with Lipschitz singularities

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2025年8月28日

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Jiao Chen,
Martin Hsu,
Fred Yu-Hsiang Lin

摘要

This paper studies the $L^{p}$ $L^{p}$ boundedness of bilinear Fourier multipliers in the local $L^{2}$ $L^{2}$ range. We assume a Hörmander condition relative to a singular set that is a finite union of Lipschitz curves. The Hörmander 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.