Fourier decay for curved Frostman measures
Shival Dasu, Ciprian Demeter
TL;DR
This paper studies how measures supported on curved geometric objects decay in the Fourier domain, using decoupling techniques to reprove a recent result related to the parabola.
Contribution
It combines decoupling methods with lower bounds for Furstenberg sets to establish Fourier decay for curved Frostman measures, providing a new proof of Orponen's result.
Findings
Fourier decay estimates for measures on curved sets
Reproof of Orponen's result for the parabola
Integration of decoupling with Furstenberg set bounds
Abstract
We investigate decoupling for Frostman measures supported on curves with nonzero curvature. We combine this tool with known lower bounds for Furstenberg sets to reprove Orponen's recent result for the parabola.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Geometric Analysis and Curvature Flows · Mathematical Approximation and Integration