Multilinear operators in harmonic analysis: Methods and applications

We first give a survey on multilinear Hilbert transforms. Then we study several variants of bilinear Hilbert transform such as bilinear Hilbert transform along two polynomials, discrete (integer) bilinear Hilbert transform along polynomials, finite field version of bilinear Radon transform, a hybrid of bilinear Hilbert transform and the paraproduct, etc. Our aim is to find operator norms of these operators: showing that they are finite or have certain decay. Applications in Roth type theorems will also be given.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2018

Author dc:creator

• Dong, Dong

Contributors dc:contributor

• Ford, Kevin
• Li, Xiaochun
• Erdogan, M. Burak
• Boca, Florin

• multilinear Hilbert transforms
• discrete operators
• Roth theorem

Statement dc:rights

• Copyright 2018 Dong Dong

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/101503

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/101503