Bilinear Hilbert transforms associated to plane curves

Abstract

We prove that the bilinear Hilbert transforms and maximal functions along certain general plane curves are bounded from $L^2(\mathbb{R})\times L^2(\mathbb{R})$ to $L^1(\mathbb{R})$.

arXiv comment26 pages

References in corpus (2)

• Uniform estimates for bilinear Hilbert transform and bilinear maximal functions associated to polynomials
• On the Boundedness of The Bilinear Hilbert Transform along "non-flat" smooth curves