Pointwise ergodic theorems for some thin subsets of primes

Abstract

We establish pointwise ergodic theorems for operators of Radon type along subsets of prime numbers of the form $\{\{{\phi }_1(n)\}<\psi (n)\}$. We achieve this by proving ${\ell }^p(\mathbb{Z})$ boundedness of $r$-variations, where $p>1$ and $r>2$.

References in corpus (2)

• Variation estimates for averages along primes and polynomials
• Polynomial Ergodic Averages Converge Rapidly: Variations on a Theorem of Bourgain