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Convergence of Marcinkiewicz Means of Integrable Functions with Respect to Two-Dimensional Vilenkin Systems

Convergence of Marcinkiewicz Means of Integrable Functions with Respect to Two-Dimensional... We prove that the maximal operator of the Marcinkiewicz mean of integrable two-variable functions is of weak type (1, 1) on bounded two-dimensional Vilenkin groups. Moreover, for any integrable function 𝑓 the Marcinkiewicz mean ॣ 𝑛 𝑓 converges to 𝑓 almost everywhere. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

Convergence of Marcinkiewicz Means of Integrable Functions with Respect to Two-Dimensional Vilenkin Systems

Georgian Mathematical Journal , Volume 11 (3) – Sep 1, 2004

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Publisher
de Gruyter
Copyright
© Heldermann Verlag
ISSN
1072-947X
eISSN
1072-9176
DOI
10.1515/GMJ.2004.467
Publisher site
See Article on Publisher Site

Abstract

We prove that the maximal operator of the Marcinkiewicz mean of integrable two-variable functions is of weak type (1, 1) on bounded two-dimensional Vilenkin groups. Moreover, for any integrable function 𝑓 the Marcinkiewicz mean ॣ 𝑛 𝑓 converges to 𝑓 almost everywhere.

Journal

Georgian Mathematical Journalde Gruyter

Published: Sep 1, 2004

Keywords: Bounded Vilenkin groups; Vilenkin series; Marcinkiewicz means; a.e. convergence; two-variable functions

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