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

Dendrinos, Spyridon; Hughes, Kevin; Vitturi, Marco


Spyridon Dendrinos

Kevin Hughes

Marco Vitturi


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.

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
Keywords Averages along curves, ℓp -improving, Diophantine equations
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