Completely bounded Paley projections on anisotropic Sobolev spaces on tori

Abstract

We study the existence of certain completely bounded Paley projection on the anisotropic Sobolev spaces on tori. Our result should be viewed as a generalization of a similar result obtained by Pełczy{ń}ski and Wojciechowski. By a transference method, we obtain similar results on the Sobolev spaces on quantum tori.