English

Pointwise ergodic theorems for some thin subsets of primes

Classical Analysis and ODEs 2019-02-15 v2 Dynamical Systems

Abstract

We establish pointwise ergodic theorems for operators of Radon type along subsets of prime numbers of the form {{φ1(n)}<ψ(n)}\big\{\{ \varphi_1(n)\} < \psi(n)\big\}. We achieve this by proving p(Z)\ell^p(\mathbb{Z}) boundedness of rr-variations, where p>1p > 1 and r>2r > 2.

Keywords

Cite

@article{arxiv.1803.05692,
  title  = {Pointwise ergodic theorems for some thin subsets of primes},
  author = {Bartosz Trojan},
  journal= {arXiv preprint arXiv:1803.05692},
  year   = {2019}
}
R2 v1 2026-06-23T00:54:03.168Z