Abstract:
Rubio de Francia proved a one-sided Littlewood-Paley inequality for the square function constructed from an arbitrary system of
disjoint intervals. Later, Osipov proved a similar inequality for Walsh systems. We prove a similar inequality for more general Vilenkin systems.
Bibliography: 11 titles.
Keywords:
Littlewood-Paley-Rubio de Francia inequality, Vilenkin systems.
This research was carried out with the financial support of the “BASIS” foundation for the advancement of theoretical physics and mathematics and a grant in the form of subsidies from the federal budget to the implementation of state support for the creation and development of world-class scientific centres, including international mathematical centres and world-class scientific centres that do research and development in areas
that are scientific and technological development priorities (agreement no. 075-15-2019-1620 of 8 November, 2019 between the Ministry of Education and Science of the Russian Federation and the St Petersburg Department of
Steklov Mathematical Institute of Russian Academy of Sciences).
\Bibitem{Tse21}
\by A.~S.~Tselishchev
\paper A~Littlewood-Paley-Rubio de~Francia inequality for bounded Vilenkin systems
\jour Sb. Math.
\yr 2021
\vol 212
\issue 10
\pages 1491--1502
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Linking options:
https://www.mathnet.ru/eng/sm9482
https://doi.org/10.1070/SM9482
https://www.mathnet.ru/eng/sm/v212/i10/p152
This publication is cited in the following 2 articles:
Viacheslav Borovitskiy, “Littlewood–Paley–Rubio de Francia inequality for multi‐parameter Vilenkin systems”, Mathematische Nachrichten, 297:3 (2024), 1092
Anton Tselishchev, “Littlewood–Paley–Rubio de Francia inequality for unbounded Vilenkin systems”, Journal of Approximation Theory, 298 (2024), 106006
Citation in format AMSBIB
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