127 citations · 1.1k across the 99 of their papers we have counts for
103 papers
Lower Estimate on Square Function of an Indicator Set
Christina Giannitsi, Michael T. Lacey
Let be a discrete martingale square function. Then, for any set of positive probability, we have for an absolute constan…
On the convergence of multiple ergodic means
Grigori A. Karagulyan, Michael T. Lacey, Vahan A. Martirosyan
Given sequence of measure preserving transformations on a measurable space . We prove a.e. convergence of the ergodic means \begin{equation} \fra…
Improving and Maximal Inequalities for Primes in Progressions
Christina Giannitsi, Michael T. Lacey, Hamed Mousavi +1
Assume that are integers, and that . Define an average along the primes in a progression of diameter , given by integer . \begin{align*} A_{N,y,b…
Endpoint improving estimates for Prime averages
Michael T. Lacey, Hamed Mousavi, Yaghoub Rahimi
Let denote von Mangoldt's function, and consider the averages \begin{align*} A_N f (x) &=\frac{1}{N}\sum_{1\leq n \leq N}f(x-n)Λ(n) . \end{align*} We prove sharp -…
A Polynomial Roth Theorem for Corners in Finite Fields
Rui Han, Michael T Lacey, Fan Yang
We prove a Roth type theorem for polynomial corners in the finite field setting. Let and be two polynomials of distinct degree. For sufficiently large primes , any s…
Compactness of commutator of Riesz transforms in the two weight setting
Michael Lacey, Ji Li
We characterize the compactness of commutators in the Bloom setting. Namely, for a suitably non-degenerate Calderón--Zygmund operator , and a pair of weights , the…