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Littlewood-Paley and Multiplier Theorems for Vilenkin-Fourier Series

Published online by Cambridge University Press:  20 November 2018

Wo-Sang Young
Wo-Sang Young*
Affiliation:
Department of Mathematics University of Alberta Edmonton, Alberta T6G 2G1
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Abstract

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Let S2jf be the 2j-th partial sum of the Vilenkin-Fourier series of f ∊ L1, and set S2-1f = 0. For , we show that the ratio

is contained between two bounds (independent of f) . From this we obtain the Marcinkiewicz multiplier theorem for Vilenkin-Fourier series.

Keywords

42C1042A4543A75
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 3 , 01 June 1994 , pp. 662 - 672
Copyright
Copyright © Canadian Mathematical Society 1994

References

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