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Smoothness conditions and integrability theorems on bounded Vilenkin groups

Bloom, W.R. and Fournier, J.J.F. (1988) Smoothness conditions and integrability theorems on bounded Vilenkin groups. Journal of the Australian Mathematical Society (Series A), 45 . pp. 46-61.

Link to Published Version: http://dx.doi.org/10.1017/S1446788700032250
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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.

Publication Type: Journal Article
Murdoch Affiliation: School of Mathematical and Physical Sciences
Publisher: Cambridge University Press
Copyright: © 1988 Australian Mathematical Society
URI: http://researchrepository.murdoch.edu.au/id/eprint/31350
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