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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2 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
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math.CA 2years
2026 2verdicts
UNVERDICTED 2representative 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.
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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.