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Title:Multilinear operators in harmonic analysis: Methods and applications
Author(s):Dong, Dong
Director of Research:Li, Xiaochun
Doctoral Committee Chair(s):Erdogan, M. Burak
Doctoral Committee Member(s):Ford, Kevin; Boca, Florin
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):multilinear Hilbert transforms
discrete operators
Roth theorem
Abstract: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.
Issue Date:2018-06-22
Type:Text
URI:http://hdl.handle.net/2142/101503
Rights Information:Copyright 2018 Dong Dong
Date Available in IDEALS:2018-09-27
Date Deposited:2018-08


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