Journal of Fourier Analysis and Applications

, Volume 21, Issue 4, pp 822–848 | Cite as

Cotlar’s Ergodic Theorem Along the Prime Numbers

  • Mariusz Mirek
  • Bartosz Trojan


The aim of this paper is to prove Cotlar’s ergodic theorem modeled on the set of primes.


Maximal truncated Hilbert transform Prime numbers Pointwise convergence 



The authors are grateful to the referees for careful reading of the manuscript and useful remarks that led to the improvement of the presentation. The authors were supported by NCN Grant DEC–2012/05/D/ST1/00053.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Mathematical InstituteUniversität BonnBonnGermany
  2. 2.Instytut MatematycznyUniwersytet WrocławskiWrocławPoland

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