Boundedness of Multilinear Hilbert Transforms Along Moment Curves

Abstract

We prove the boundedness of multilinear Hilbert transforms along moment curves by establishing uniform estimates for both translated and untranslated multilinear paraproducts and by applying a Sobolev smoothing inequality. As a byproduct of our method, we obtain the same bounds for multilinear maximal functions along moment curves.

arXiv commentThe lower bound 1/3 for r in the first version is corrected to 1/2 due to counterexamples, which are provided. A uniform estimate for the corresponding multilinear Hilbert transform is added. Some typos are corrected, and more details are added to the proofs of several lemmas