Skip to main content

Research Repository

Advanced Search

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.


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.

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
Public URL


You might also like

Downloadable Citations