Spyridon Dendrinos
Some Subcritical Estimates for the ℓp-Improving Problem for Discrete Curves
Dendrinos, Spyridon; Hughes, Kevin; Vitturi, Marco
Authors
Kevin Hughes
Marco Vitturi
Abstract
We apply Christ’s method of refinements to the ℓ^p-improving problem for discrete averages AN along polynomial curves in Z^d. Combined with certain elementary estimates for the number of solutions to certain special systems of diophantine equations, we obtain some restricted weak-type p→p′ estimates for the averages A_N in the subcritical regime. The dependence on N of the constants here obtained is sharp, except maybe for an ϵ-loss.
Citation
Dendrinos, S., Hughes, K., & Vitturi, M. (2022). Some Subcritical Estimates for the ℓp-Improving Problem for Discrete Curves. Journal of Fourier Analysis and Applications, 28(4), Article 69. https://doi.org/10.1007/s00041-022-09958-y
Journal Article Type | Article |
---|---|
Acceptance Date | Jun 3, 2022 |
Online Publication Date | Aug 5, 2022 |
Publication Date | 2022-08 |
Deposit Date | Dec 2, 2022 |
Publicly Available Date | Dec 2, 2022 |
Journal | Journal of Fourier Analysis and Applications |
Print ISSN | 1069-5869 |
Electronic ISSN | 1531-5851 |
Publisher | Springer |
Peer Reviewed | Peer Reviewed |
Volume | 28 |
Issue | 4 |
Article Number | 69 |
DOI | https://doi.org/10.1007/s00041-022-09958-y |
Keywords | Averages along curves, ℓp -improving, Diophantine equations |
Public URL | http://researchrepository.napier.ac.uk/Output/2965317 |
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Some Subcritical Estimates For The ℓp-Improving Problem For Discrete Curves
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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/
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