Develops a quantitative flatness framework to obstruct Fourier restriction, L^p-improving, and Fourier decay estimates for measures, applied to bound Fourier dimensions of surfaces, curves, Patterson-Sullivan measures, and self-affine sets.
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3 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
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math.CA 3years
2026 3verdicts
UNVERDICTED 3representative citing papers
A new restriction theorem is established that uses L^q-dimensions to obtain a continuum of Fourier restriction estimates recovering Stein-Tomas at q=∞ via complex interpolation, with improvements shown for certain multifractal measures.
Borel sets with Fourier dimension at least 2 have distance sets of full Hausdorff dimension in any ambient dimension d, and sets with Fourier spectrum at least d/4 + 1 at theta = 1/2 also achieve this even when their Fourier dimension is zero provided d is at least 4.
citing papers explorer
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Quantitative flatness and obstructions in Fourier analysis
Develops a quantitative flatness framework to obstruct Fourier restriction, L^p-improving, and Fourier decay estimates for measures, applied to bound Fourier dimensions of surfaces, curves, Patterson-Sullivan measures, and self-affine sets.
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Fourier restriction estimates based on $L^q$-dimensions: beyond Stein--Tomas
A new restriction theorem is established that uses L^q-dimensions to obtain a continuum of Fourier restriction estimates recovering Stein-Tomas at q=∞ via complex interpolation, with improvements shown for certain multifractal measures.
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On Fourier decay and the distance set problem
Borel sets with Fourier dimension at least 2 have distance sets of full Hausdorff dimension in any ambient dimension d, and sets with Fourier spectrum at least d/4 + 1 at theta = 1/2 also achieve this even when their Fourier dimension is zero provided d is at least 4.