5 papers
On the resonant Carleson-Radon transform in all dimensions. The degree one resonant case
Martin Hsu, Victor Lie
In this paper, we provide the resolution of the degree one resonant case in all dimensions. Our main result reads as follows: for any dimension set $\mathbf{X}(\mathbf{t}…
On a Carleson-Radon Transform (the non-resonant setting)
Martin Hsu, Victor Lie
Given a curve with , we define the Carleson-Radon transform along by the formula $$ C_{[\vecα]}…
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…