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arXiv · 1803.05692

Pointwise ergodic theorems for some thin subsets of primes

Bartosz Trojan
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Abstract

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

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Bartosz Trojan. 2018-03-15. Pointwise ergodic theorems for some thin subsets of primes. https://arxiv.org/abs/1803.05692

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