J Austral Math Soc Ser A 45 pp46--61, 1988.

Smoothness Conditions and Integrability Theorems of Bounded Vilenkin Groups

Walter R. Bloom and John J. F. Fournier

Abstract

Various criteria, in terms of forward differences and related operations on coefficients, are shown to imply that certain series on bounded Vilenkin groups represent integrable functions. These results include analogues of known integrability theorems for trigonometric series. The method of proof is to pass from the given series to a derived series, and to deduce the integrability of the original series from smoothness properties of the latter.

1980 AMS Subject Classification: primary 42C10; secondary 43A50, 43A70

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Authors

Walter R. Bloom

School of Mathematical and Physical Sciences, Murdoch University, Perth, Western Australia 6150, Australia.

John J. F. Fournier

Department of Mathematics, University of British Colombia, Vancouver, Canada, V6T 1Y4.