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arXiv · 2108.04147

Discrete multilinear maximal functions and number theory

Theresa C. Anderson
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Abstract

Many multilinear discrete operators are primed for pointwise decomposition; such decompositions give structural information but also an essentially optimal range of bounds. We study the (continuous) slicing method of Jeong and Lee -- which when debuted instantly gave sharp multilinear operator bounds -- in the discrete setting. Via several examples, number theoretic connections, pointed commentary, and a unified theory we hope that this useful technique will lead to further applications. This work generalizes, and was inspired by, the author's work with Palsson on a special case.

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Theresa C. Anderson. 2021-08-09. Discrete multilinear maximal functions and number theory. https://arxiv.org/abs/2108.04147

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