Averages Along the Primes: Improving and Sparse Bounds

Rui Han, Ben Krause, Michael Lacey +1

Consider averages along the prime integers $\mathbb{P}$ given by \begin{equation*} \mathcal{A}_N f (x) = N ^{-1} \sum_{ p \in \mathbb P \;:\; p\leq N} (\log p) f (x-p). \end{equat…