4 papers
Rough averages of triangular Hilbert transforms
Fred Yu-Hsiang Lin, Lenka Slavíková
We study a bilinear singular integral operator obtained by taking rough averages of certain directional variants of the triangular Hilbert transform. This operator can be interpret…
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(…
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…
A study guide for "Trilinear smoothing inequalities and a variant of the triangular Hilbert transform"
Martin Hsu, Fred Yu-Hsiang Lin, Amelia Stokolosa
This article is a study guide for "Trilinear smoothing inequalities and a variant of the triangular Hilbert transform" by Christ, Durcik, and Roos. We first present the standard te…