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

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...

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Bibliographic Details
Published in:Journal of approximation theory 2024-03, Vol.298, p.106006, Article 106006
Main Author: Tselishchev, Anton
Format: Article
Language:English
Subjects:
Fourier multipliers
Littlewood–Paley theory
Rubio de Francia inequality
Vilenkin systems
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Summary: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.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2023.106006