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Scaled Oscillation and Level Sets
Iqra Altaf, Marianna Csornyei, Bobby Wilson
We study the size and regularity properties of level sets of continuous functions with bounded upper-scaled and lower-scaled oscillation.
Weighted restriction estimates and application to Falconer distance set problem
Xiumin Du, Larry Guth, Yumeng Ou +3
We prove some weighted Fourier restriction estimates using polynomial partitioning and refined Strichartz estimates. As application we obtain improved spherical average decay rates…
Sets with Arbitrarily Slow Favard Length Decay
Bobby Wilson
In this article, we consider the concept of the decay of the Favard length of -neighborhoods of purely unrectifiable sets. We construct non-self-similar Cantor sets fo…
On almost everywhere convergence of strong arithmetic means of Fourier series
Bobby Wilson
This article establishes a real-variable argument for Zygmund's theorem on almost everywhere convergence of strong arithmetic means of partial sums of Fourier series on $\mathbb{T}…