Some Subcritical Estimates for the ℓp-Improving Problem for Discrete Curves

Dendrinos, Spyridon; Hughes, Kevin; Vitturi, Marco

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