5 papers · 1 filter
Additive energy of regular measures in one and higher dimensions, and the fractal uncertainty principle
Laura Cladek, Terence Tao
We obtain new bounds on the additive energy of (Ahlfors-David type) regular measures in both one and higher dimensions, which implies expansion results for sums and products of the…
Upper and lower bounds on the rate of decay of the Favard curve length for the four-corner Cantor set
Laura Cladek, Blair Davey, Krystal Taylor
The Favard length of a subset of the plane is defined as the average of its orthogonal projections. This quantity is related to the probabilistic Buffon needle problem; that is, th…
Directional maximal function along the primes
Laura Cladek, Polona Durcik, Ben Krause +1
We study a two-dimensional discrete directional maximal operator along the set of the prime numbers. We show existence of a set of vectors, which are lattice points in a sufficient…
Discrete Analogues in Harmonic Analysis: Directional Maximal Functions in
Laura Cladek, Ben Krause
Let be a collection of vectors that live near a discrete sphere. We consider discrete directional maximal functions on where the set of…
A Discrete Carleson Theorem Along the Primes with a Restricted Supremum
Laura Cladek, Kevin Henriot, Ben Krause +2
Consider the discrete maximal function acting on finitely supported functions on the integers, \[ \mathcal{C}_Λf(n) := \sup_{λ\in Λ} | \sum_{p \in \pm \mathbb{P}} f(n-p) \log |p| \…