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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2201.09649 |
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Table of Contents:
- 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.