A sharp H\'{o}rmander condition for bilinear Fourier multipliers with Lipschitz singularities
- Resource Type
- Working Paper
- Authors
- Chen, Jiao; Hsu, Martin; Lin, Fred Yu-Hsiang
- Source
- Subject
- Mathematics - Classical Analysis and ODEs
- Language
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.