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arXiv · 2007.10249

On superorthogonality

Lillian B. Pierce
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Abstract

In this survey, we explore how superorthogonality amongst functions in a sequence $f_1,f_2,f_3,\ldots$ 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.

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Lillian B. Pierce. 2020-07-20. On superorthogonality. https://arxiv.org/abs/2007.10249

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