On the Littlewood--Paley--Rubio de Francia inequality for the bounded Vilenkin systems
Anton Tselishchev
TL;DR
This paper extends the Littlewood--Paley--Rubio de Francia inequality to a broader class of Vilenkin systems, generalizing previous results for Walsh functions and arbitrary intervals.
Contribution
It proves the inequality for general Vilenkin systems, broadening the scope beyond Walsh functions and specific interval cases.
Findings
Inequality holds for general Vilenkin systems
Extends previous results for Walsh functions
Generalizes Littlewood--Paley--Rubio de Francia inequality
Abstract
The one-sided Littlewood--Paley inequality for arbitrary intervals was proved by Rubio de Francia. Later, N. Osipov proved its analogue for the system of Walsh functions. In this paper, this inequality is proved for more general Vilenkin systems.
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