5 papers · 1 filter
Endpoint Estimates for Stein's Purely Quadratic Carleson Operator
Anastasios Fragkos, Ben Krause, Michael Lacey
We study the near 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…
Polynomial Ergodic Averages Along Short Intervals
Anastasios Fragkos, Hamed Mousavi, Amelia Stokolosa
We study pointwise convergence of polynomial ergodic averages over short intervals whose left endpoints tend to infinity. For a polynomial orbit of degree and doubly lacun…
A Variation Norm Carleson Theorem Along the Primes
Anastasios Fragkos, Ben Krause, Nazar Miheisi +1
Let denote the von Mangoldt function; we prove that for each , there exist constants \[ r' < \mathbf{c}(r) < 2 < \mathbf{C}(r), \qquad \lim_{r \to \infty} \mathbf{c}(r)…
Multilinear Wavelet Compact T(1) Theorem
Anastasios Fragkos, A. Walton Green, Brett D. Wick
We prove a wavelet theorem for compactness of multilinear Calderón-Zygmund (CZ) operators. Our approach characterizes compactness in terms of testing conditions and yields a…
The weak-type Carleson theorem via wave packet estimates
Francesco Di Plinio, Anastasios Fragkos
We prove that the weak- norms, and in fact the sparse -norms, of the Carleson maximal partial Fourier sum operator are as . This is an…