Estimates of spherial averages of Fourier transforms and dimensions of sets

DOI10.1112/S0025579300007087zbMath0789.28006OpenAlexW2042871088MaRDI QIDQ4287332

Per Sjoelin

Publication date: 16 June 1994

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/s0025579300007087

zbMATH Keywords

Fourier transformsHausdorff dimensionSalem setenergy of measuresdimension of sets

Mathematics Subject Classification ID

Length, area, volume, other geometric measure theory (28A75) Hausdorff and packing measures (28A78)

Related Items (15)

On the capacity of sets of divergence associated with the spherical partial integral operator ⋮ Spherical harmonics and spherical averages of Fourier transforms ⋮ Regularity of Distance Measures and Sets ⋮ Rigidity, Graphs and Hausdorff Dimension ⋮ On Falconer's distance set conjecture ⋮ On the dimension of divergence sets of dispersive equations ⋮ Weighted Fourier extension estimates and applications ⋮ Examples of measures with slow decay of the spherical means of the Fourier transform ⋮ Average decay of the Fourier transform of measures with applications ⋮ Fourier decay of fractal measures on hyperboloids ⋮ An \(L^2\)-identity and pinned distance problem ⋮ Improved decay of conical averages of the Fourier transform ⋮ Fourier restriction in low fractal dimensions ⋮ Improved bounds for restricted projection families via weighted Fourier restriction ⋮ Randomised circular means of Fourier transforms of measures

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