31 citations · 128 across the 29 of their papers we have counts for
4 papers · 1 filter
On Convergence of Oscillatory Ergodic Hilbert Transforms
Ben Krause, Michael Lacey, Máté Wierdl
We introduce sufficient conditions on discrete singular integral operators for their maximal truncations to satisfy a sparse bound. The latter imply a range of quantitative weighte…
Sparse Bounds for Random Discrete Carleson Theorems
Ben Krause, Michael T. Lacey
We study discrete random variants of the Carleson maximal operator. Intriguingly, these questions remain subtle and difficult, even in this setting. Let be an independent…
Sparse Bounds for Maximal Monomial Oscillatory Hilbert Transforms
Ben Krause, Michael T. Lacey
For each , the Hilbert transform with a polynomial oscillation as below satisfies a sparse bound, for all $$ H _{ \ast } f (x) = \sup _{ε} \Bigl\lvert…
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| \…