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

Spyridon Dendrinos; Kevin Hughes; Marco Vitturi

doi:10.1007/s00041-022-09958-y

Some Subcritical Estimates for the ℓ^p -Improving Problem for Discrete Curves

Spyridon Dendrinos
, Kevin Hughes
, Marco Vitturi

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

We apply Christ’s method of refinements to the ℓ^p-improving problem for discrete averages A_N 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.

Original language	English
Article number	69
Journal	Journal of Fourier Analysis and Applications
Volume	28
Issue number	4
DOIs	https://doi.org/10.1007/s00041-022-09958-y
Publication status	Published - Aug 2022

Keywords

Averages along curves
Diophantine equations
ℓ-improving

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abstract = "We apply Christ{\textquoteright}s method of refinements to the ℓp-improving problem for discrete averages AN along polynomial curves in Zd. 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 AN in the subcritical regime. The dependence on N of the constants here obtained is sharp, except maybe for an ϵ-loss.",

keywords = "Averages along curves, Diophantine equations, ℓ-improving",

author = "Spyridon Dendrinos and Kevin Hughes and Marco Vitturi",

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AU - Hughes, Kevin

AU - Vitturi, Marco

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Y1 - 2022/8

N2 - We apply Christ’s method of refinements to the ℓp-improving problem for discrete averages AN along polynomial curves in Zd. 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 AN in the subcritical regime. The dependence on N of the constants here obtained is sharp, except maybe for an ϵ-loss.

AB - We apply Christ’s method of refinements to the ℓp-improving problem for discrete averages AN along polynomial curves in Zd. 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 AN in the subcritical regime. The dependence on N of the constants here obtained is sharp, except maybe for an ϵ-loss.

KW - Averages along curves

KW - Diophantine equations

KW - ℓ-improving

UR - https://www.scopus.com/pages/publications/85135488526

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DO - 10.1007/s00041-022-09958-y

M3 - Article

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JF - Journal of Fourier Analysis and Applications

IS - 4

M1 - 69

ER -

Some Subcritical Estimates for the ℓ^p -Improving Problem for Discrete Curves

Abstract

Keywords

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