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# Title: Variational estimates for discrete operators modeled on multi-dimensional polynomial subsets of primes

Abstract: We prove the extensions of Birkhoff's and Cotlar's ergodic theorems to multi-dimensional polynomial subsets of prime numbers $\mathbb{P}^k$. We deduce them from $\ell^p$-boundedness of $r$-variational seminorms for the corresponding discrete operators of Radon type, where $p > 1$ and $r > 2$.
 Subjects: Classical Analysis and ODEs (math.CA) Cite as: arXiv:1803.05406 [math.CA] (or arXiv:1803.05406v1 [math.CA] for this version)

## Submission history

From: Bartosz Trojan [view email]
[v1] Wed, 14 Mar 2018 17:08:58 GMT (34kb)