Measure and dimension of sums and products

DOI10.1090/proc/15513zbMath1471.28005arXiv1810.11553OpenAlexW3173898637MaRDI QIDQ5002542

Kyle Hambrook, Krystal Taylor

Publication date: 28 July 2021

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

Full work available at URL: https://arxiv.org/abs/1810.11553

zbMATH Keywords

Hausdorff dimensionFourier dimensionfractalsMinkowski sumMinkowski product

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Fractals (28A80) Hausdorff and packing measures (28A78)

Related Items (1)

Dimension and measure of sums of planar sets and curves

Cites Work

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• Averages in the plane over convex curves and maximal operators
• The discretized sum-product and projection theorems
• Unions of hyperplanes, unions of spheres, and some related estimates
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• Sets of Salem type and sharpness of the 𝐿²-Fourier restriction theorem
• Sharpness of the Mockenhaupt–Mitsis–Bak–Seeger restriction theorem in higher dimensions
• Packing spheres and fractal Strichartz estimates in $\mathbb {R}^d$ for $d\geq 3$
• Packing Circles in the Plane
• Spherical averages of Fourier transforms of measures with finite energy; dimensions of intersections and distance sets
• Maximal functions: Spherical means
• A Kakeya-type problem for circles
• Interior of sums of planar sets and curves
• Fourier Analysis and Hausdorff Dimension
• Salem sets and restriction properties of Fourier transforms

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