Bilinear Hilbert transforms along curves I. The monomial case

2008/05/01 by Li, Xiaochun · 2 citations
#42B20 #42B25 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.0805.0107

Abstract

We establish an L² × L² to L¹ estimate for the bilinear Hilbert transform along a curve defined by a monomial. Our proof is closely related to multi-linear oscillatory integrals.

Cited by

• On the boundedness of the curved trilinear Hilbert transform and the curved n-linear maximal operator in the quasi-Banach regime
• On Multi-linear Maximal Operators Along Homogeneous Curves

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