4 papers
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| \…