Averages in vector spaces over finite fields

DOI10.1017/S0305004107000680zbMath1141.43006MaRDI QIDQ5450699

Anthony Carbery, Brendan Stones, James Wright

Publication date: 13 March 2008

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

zbMATH Keywords

finite fieldmaximal average\((L^p, L^q)\) boundedness

Mathematics Subject Classification ID

Harmonic analysis in several variables (42B99) Abstract harmonic analysis (43A99) Character groups and dual objects (43A40)

Related Items (6)

Averaging operators over homogeneous varieties over finite fields ⋮ Sharp $L^p\rightarrow L^r$ estimates for $k$-plane transforms in finite fields ⋮ Averages and maximal averages over Product \(j\)-varieties in finite fields ⋮ From oscillatory integrals and sublevel sets to polynomial congruences and character sums ⋮ Restricted averaging operators to cones over finite fields ⋮ Sharp endpoint estimates for the $X$-ray transform and the Radon transform in finite fields

Cites Work

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• Degenerate Fourier integral operators in the plane
• On continuum incidence problems related to harmonic analysis.
• La conjecture de Weil. I
• Restriction and Kakeya phenomena for finite fields
• A sum-product estimate in finite fields, and applications
• 𝐿^{𝑝} improving bounds for averages along curves
• On Some Exponential Sums
• Bounds for exponential sums

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