A new proof of an inequality of Bourgain
Polona Durcik, Joris Roos
TL;DR
This paper presents an alternative proof of Bourgain's trilinear smoothing inequality by applying recent additive combinatorics techniques developed by Peluse and Peluse-Prendiville.
Contribution
It introduces a novel application of additive combinatorics methods to provide a new proof of an existing inequality by Bourgain.
Findings
Successful application of additive combinatorics techniques to harmonic analysis
New proof of Bourgain's trilinear smoothing inequality
Demonstrates versatility of additive combinatorics methods
Abstract
The purpose of this short note is to demonstrate how some techniques from additive combinatorics recently developed by Peluse and Peluse-Prendiville can be applied to give an alternative proof for a trilinear smoothing inequality originally due to Bourgain.
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Taxonomy
TopicsPoint processes and geometric inequalities · Limits and Structures in Graph Theory · graph theory and CDMA systems