Littlewood--Paley--Rubio de Francia inequality for unbounded Vilenkin systems

Abstract

Rubio de Francia proved the one-sided version of Littlewood--Paley inequality for arbitrary intervals. In this paper, we prove the similar inequality in the context of arbitrary Vilenkin systems (that is, for functions on infinite products of cyclic groups). There are no assumptions on the orders of these groups.

arXiv comment31 pages