Finite Riesz products and Ornstein non-inequalities on quantum tori

Abstract

We demonstrate a construction of products on the quantum torus ${\mathbb{T}}_{\theta }^2$ that generalises the usual construction of finite Riesz products on the commutative torus ${\mathbb{T}}^2$. We explain why the former constitutes a natural analogue of the latter in the non-commutative setting and, based on this construction, as well as on previous results by K. Kazaniecki and the second author, we prove a non-commutative version of an Ornstein non-inequality.

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