Cohomological equations for suspension flows over Vershik automorphisms

In this paper we give sufficient conditions for existence of a solution of cohomological equation for suspension flows over automorphisms of Markov compacta, which were introduced by Vershik and Ito. The main result (Theorem 1) can be regarded as a symbolic analogue of results due to Forni and Marmi, Moussa and Yoccoz for translation flows and interval exchange transformations.