31 citations · 128 across the 29 of their papers we have counts for
5 papers · 1 filter
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…
A Non-Linear Roth Theorem for Fractals of Sufficiently Large Dimension
Ben Krause
Suppose that , and that has sufficiently large dimension, . Then for any polynomial of degree with no constant term, th…
Discrete Fractional Integration Operators Along the Primes
Ben Krause
We prove that the discrete fractional integration operators along the primes \[ T^λ_{\mathbb{P}}f(x) := \sum_{p} \frac{f(x-p)}{p^λ} \cdot \log p \] are bounded $\ell^p\to \ell^{p'}…
A Non-Linear Roth Theorem for Sets of Positive Density
Ben Krause
Suppose that has positive upper density, \[ \limsup_{|I| \to \infty} \frac{|A \cap I|}{|I|} = δ> 0,\] and is a polynomial with no co…
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…