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

Anton Tselishchev

doi:10.1016/j.jat.2023.106006

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

Anton Tselishchev

Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

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.

Originalsprache	Englisch
Aufsatznummer	106006
Seitenumfang	31
Fachzeitschrift	Journal of Approximation Theory
Volume	298
Ausgabenummer	298
DOIs	https://doi.org/10.1016/j.jat.2023.106006
Publikationsstatus	Veröffentlicht - März 2024

Wissenschaftszweige

101002 Analysis
101032 Funktionalanalysis

JKU-Schwerpunkte

Digital Transformation

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10.1016/j.jat.2023.106006

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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.",

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AB - 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.

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