Upper bounds for Fourier decay rates of fractal measures

DOI10.1112/jlms.12364zbMath1462.42016arXiv1908.05753OpenAlexW2968995638MaRDI QIDQ3389195

Xiumin Du

Publication date: 10 May 2021

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

Full work available at URL: https://arxiv.org/abs/1908.05753

zbMATH Keywords

average decay rates of the Fourier transform of fractal measure

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Harmonic analysis and PDEs (42B37)

Related Items (8)

Pointwise convergence over fractals for dispersive equations with homogeneous symbol ⋮ Weighted Fourier extension estimates and applications ⋮ Counterexamples for the fractal Schrödinger convergence problem with an intermediate space trick ⋮ Fourier decay of fractal measures on hyperboloids ⋮ An improved result for Falconer's distance set problem in even dimensions ⋮ Dimension of divergence set of the wave equation ⋮ Hausdorff dimension and projections related to intersections ⋮ Convergence over fractals for the Schroedinger equation

Cites Work

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• An \(L^2\)-identity and pinned distance problem
• On Falconer's distance set problem in the plane
• Sharp \(L^2\) estimates of the Schrödinger maximal function in higher dimensions
• On the Hausdorff dimensions of distance sets
• Spherical averages of Fourier transforms of measures with finite energy; dimensions of intersections and distance sets
• Fourier Analysis and Hausdorff Dimension
• Some special solutions of the Schr\"odinger equation

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