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math.CA2024
Smoothing inequalities for corner-type bilinear averages: geometric characterization and applications
Martin Hsu, Fred Yu-Hsiang Lin
We study Sobolev smoothing inequalities for bilinear averages associated with corner-type configurations \[ A_{γ,ρ}(f_1,f_2)(x_1,x_2) =\int f_1(x_1+γ_1(t),x_2)f_2(x_1,x_2+γ_2(t))ρ(…
math.CA2024
A sharp Hörmander condition for bilinear Fourier multipliers with Lipschitz singularities
Jiao Chen, Martin Hsu, Fred Yu-Hsiang Lin
This paper studies the boundedness of bilinear Fourier multipliers in the local range. We assume a Hörmander condition relative to a singular set that is a finite u…