On Superorthogonality

Journal Article (Journal Article)

In this survey, we explore how superorthogonality amongst functions in a sequence f1, f2, f3, … results in direct or converse inequalities for an associated square function. We distinguish between three main types of superorthogonality, which we demonstrate arise in a wide array of settings in harmonic analysis and number theory. This perspective gives clean proofs of central results, and unifies topics including Khintchine’s inequality, Walsh–Paley series, discrete operators, decoupling, counting solutions to systems of Diophantine equations, multicorrelation of trace functions, and the Burgess bound for short character sums.

Full Text

Duke Authors

Cited Authors

  • Pierce, LB

Published Date

  • July 1, 2021

Published In

Volume / Issue

  • 31 / 7

Start / End Page

  • 7096 - 7183

International Standard Serial Number (ISSN)

  • 1050-6926

Digital Object Identifier (DOI)

  • 10.1007/s12220-021-00606-3

Citation Source

  • Scopus