Improved decay of conical averages of the Fourier transform

DOI10.1090/proc/14747zbMath1423.42047arXiv1806.08051OpenAlexW3101750361WikidataQ127461571 ScholiaQ127461571MaRDI QIDQ5234971

Terence L. J. Harris

Publication date: 7 October 2019

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

Full work available at URL: https://arxiv.org/abs/1806.08051

Mathematics Subject Classification ID

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

Related Items (12)

A cone restriction estimate using polynomial partitioning ⋮ Pointwise convergence of sequential Schrödinger means ⋮ Fourier decay of fractal measures on surfaces of co-dimension two in \(\mathbb{R}^5\) ⋮ Improved local smoothing estimate for the wave equation in higher dimensions ⋮ Fourier decay of fractal measures on hyperboloids ⋮ Dimension of divergence set of the wave equation ⋮ On smoothing estimates in modulation spaces and the nonlinear Schrödinger equation with slowly decaying initial data ⋮ Hausdorff dimension and projections related to intersections ⋮ Circular average relative to fractal measures ⋮ \(L^p\)-\(L^q\) local smoothing estimates for the wave equation via \(k\)-broad Fourier restriction ⋮ Fourier restriction in low fractal dimensions ⋮ Improved bounds for restricted projection families via weighted Fourier restriction

Cites Work

• Application of a Fourier restriction theorem to certain families of projections in \(\mathbb R^3\)
• Fractal Strichartz estimate for the wave equation
• Restriction estimates using polynomial partitioning. II
• An \(L^2\)-identity and pinned distance problem
• A note on the Fourier transform of fractal measures
• A cone restriction estimate using polynomial partitioning
• Sharp \(L^2\) estimates of the Schrödinger maximal function in higher dimensions
• The proof of the \(l^2\) decoupling conjecture
• Spherical averages of Fourier transforms of measures with finite energy; dimensions of intersections and distance sets
• Estimates of spherial averages of Fourier transforms and dimensions of sets
• Decay of the Fourier Transform
• Weighted restriction estimates and application to Falconer distance set problem
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