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On Superorthogonality

Publication ,  Journal Article
Pierce, LB
Published in: Journal of Geometric Analysis
July 1, 2021

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.

Duke Scholars

Published In

Journal of Geometric Analysis

DOI

ISSN

1050-6926

Publication Date

July 1, 2021

Volume

31

Issue

7

Start / End Page

7096 / 7183

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0101 Pure Mathematics
 

Citation

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Chicago
ICMJE
MLA
NLM
Pierce, L. B. (2021). On Superorthogonality. Journal of Geometric Analysis, 31(7), 7096–7183. https://doi.org/10.1007/s12220-021-00606-3
Pierce, L. B. “On Superorthogonality.” Journal of Geometric Analysis 31, no. 7 (July 1, 2021): 7096–7183. https://doi.org/10.1007/s12220-021-00606-3.
Pierce LB. On Superorthogonality. Journal of Geometric Analysis. 2021 Jul 1;31(7):7096–183.
Pierce, L. B. “On Superorthogonality.” Journal of Geometric Analysis, vol. 31, no. 7, July 2021, pp. 7096–183. Scopus, doi:10.1007/s12220-021-00606-3.
Pierce LB. On Superorthogonality. Journal of Geometric Analysis. 2021 Jul 1;31(7):7096–7183.
Journal cover image

Published In

Journal of Geometric Analysis

DOI

ISSN

1050-6926

Publication Date

July 1, 2021

Volume

31

Issue

7

Start / End Page

7096 / 7183

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0101 Pure Mathematics