Application of a Fourier restriction theorem to certain families of projections in \(\mathbb R^3\)

DOI10.1007/s12220-014-9480-7zbMath1321.42021arXiv1307.5039OpenAlexW1970470390MaRDI QIDQ490757

Richard Oberlin, Daniel M. Oberlin

Publication date: 28 August 2015

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.5039

zbMATH Keywords

projectionsHausdorff dimensionFourier restriction theoremfractal measures

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Fractals (28A80) Miscellaneous topics in measure theory (28E99) Hausdorff and packing measures (28A78)

Related Items (10)

Dimension distortion by right coset projections in the Heisenberg group ⋮ On restricted families of projections in ℝ³ ⋮ Restricted families of projections onto planes: the general case of nonvanishing geodesic curvature ⋮ Average decay of the Fourier transform of measures with applications ⋮ Hausdorff Dimension, Projections, Intersections, and Besicovitch Sets ⋮ Fourier decay of fractal measures on hyperboloids ⋮ Sixty Years of Fractal Projections ⋮ Improved decay of conical averages of the Fourier transform ⋮ Hausdorff dimension and projections related to intersections ⋮ Improved bounds for restricted projection families via weighted Fourier restriction

Cites Work

• Unnamed Item
• A note on the Fourier transform of fractal measures
• Hausdorff dimension estimates for restricted families of projections in \(\mathbb{R}^3\)
• On restricted families of projections in ℝ³
• Hausdorff dimension and the exceptional set of projections
• Restricting Fourier Transforms of Measures to Curves in ℝ²
• On Hausdorff dimension of projections

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