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

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