Reinforcing a Philosophy: A counting approach to square functions over local fields
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866918327934255104 |
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| author | Biggs, Kirsti D. Brandes, Julia Hughes, Kevin |
| author_facet | Biggs, Kirsti D. Brandes, Julia Hughes, Kevin |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_09649 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Reinforcing a Philosophy: A counting approach to square functions over local fields Biggs, Kirsti D. Brandes, Julia Hughes, Kevin Classical Analysis and ODEs Number Theory 42B20, 42B25, 11D45, 11D88 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. |
| title | Reinforcing a Philosophy: A counting approach to square functions over local fields |
| topic | Classical Analysis and ODEs Number Theory 42B20, 42B25, 11D45, 11D88 |
| url | https://arxiv.org/abs/2201.09649 |