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arXiv · 2201.09649

Reinforcing a Philosophy: A counting approach to square functions over local fields

Kirsti D. Biggs·Julia Brandes·Kevin Hughes
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Abstract

In this paper, we study square functions for extension operators over finite-type, planar curves endowed with the Euclidean arclength measure. We prove new results for curves of the form $(T,ϕ(T))$ where $ϕ(T)$ is a polynomial of degree at least 2. This includes new estimates for such curves given by monomials $ϕ(T) = T^k$ for $k \geq 3$ which are uniform over all local fields whose characteristic is coprime to \(k\). Key to our approach is a systematic analysis of the second order differencing polynomial and its geometry in local fields.

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Kirsti D. Biggs, Julia Brandes, Kevin Hughes. 2026-02-09. Reinforcing a Philosophy: A counting approach to square functions over local fields. https://arxiv.org/abs/2201.09649

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