Ben Krause

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math.CA2026

Bourgain's Lambda(p) selection theorem: a greedy proof with polynomial failure bounds

Will Burstein, Alex Iosevich, Ben Krause

We give a self-contained proof of Bourgain's finite $Λ (p)$ selection theorem with an explicit probability bound. For every $p > 2$ and $N \geq 2$ , given $N$ pairwise orthogonal function…

math.CA2026

Endpoint Estimates for Stein's Purely Quadratic Carleson Operator

Anastasios Fragkos, Ben Krause, Michael Lacey

We study the near $L^{1}$ behavior of the maximally quadratically modulated Hilbert transform \[ \mathcal{C}_2f(x) := \sup_λ \left|\operatorname{p.v.} \int_{\mathbb{R}}f(x-y)e^{2 πi…

math.CA2026

A Variation Norm Carleson Theorem Along the Primes

Anastasios Fragkos, Ben Krause, Nazar Miheisi +1

Let $Λ$ denote the von Mangoldt function; we prove that for each $r > 2$ , there exist constants \[ r' < \mathbf{c}(r) < 2 < \mathbf{C}(r), \qquad \lim_{r \to \infty} \mathbf{c}(r)…

math.CA2025

An Approach To Endpoint Problems in Oscillatory Singular Integrals

Alex Iosevich, Ben Krause, Hamed Mousavi

In this note we provide a quick proof that maximal truncations of oscillatory singular integrals are bounded from $L^{1} (R)$ to $L^{1, \infty} (R)$ . The methods we us…