Circular averages and Falconer/Erdös distance conjecture in the plane for random metrics

DOI10.1090/S0002-9939-04-07603-8zbMath1096.28004arXivmath/0305132OpenAlexW1586623789WikidataQ123329153 ScholiaQ123329153MaRDI QIDQ4819722

Alexander Iosevich, Steven Hofmann

Publication date: 5 October 2004

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

Full work available at URL: https://arxiv.org/abs/math/0305132

zbMATH Keywords

Erdős conjecturedistance setFalconer conjecture

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Length, area, volume, other geometric measure theory (28A75) Erd?s problems and related topics of discrete geometry (52C10) Hausdorff and packing measures (28A78)

Related Items (17)

Discrete maximal operators over surfaces of higher codimension ⋮ On sets of directions determined by subsets of \(\mathbb R^d\) ⋮ On Falconer's distance set conjecture ⋮ Examples of measures with slow decay of the spherical means of the Fourier transform ⋮ Average decay of the Fourier transform of measures with applications ⋮ Scaling scenery of \((\times m, \times n)\) invariant measures ⋮ On the Approximate Unit Distance Problem ⋮ Fourier decay of fractal measures on hyperboloids ⋮ On the set of distances between two sets over finite fields ⋮ Sharpness of Falconer's (d+1)/2 estimate ⋮ On Falconer's distance set problem in the plane ⋮ An improved result for Falconer's distance set problem in even dimensions ⋮ On some generalisations of the Erdős distance problem over finite fields ⋮ Geometric incidence theorems via Fourier analysis ⋮ From harmonic analysis to arithmetic combinatorics ⋮ Three-point configurations determined by subsets of \({\mathbb{F}_q}^2\) via the Elekes-Sharir paradigm ⋮ Sharpness of Falconer’s Estimate and the Single Distance Problem in $$\mathbb{Z}_{q}^{d}$$

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