caa a22 4500 38630761X CHVBK 20180307111534.0 cr unu---uuuuu 161130e198808 xx s 000 0 eng 10.1017/S1446788700032250 doi S1446788700032250 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700032250 Smoothness conditions and integrability theorems on bounded Vilenkin groups [Elektronische Daten] 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. Copyright © Australian Mathematical Society 1988 primary 42 C 10 nationallicence secondary 43 A 50 nationallicence 43 A 70 nationallicence Bloom Walter R. School of Mathematical and Physical Sciences Murdoch University Perth, Western Australia 6150, Australia Fournier John J. F. Department of Mathematics University of British Columbia Vancouver, Canada V6T 1Y4 Journal of the Australian Mathematical Society Cambridge University Press 45/1(1988-08), 46-61 1446-7887 45:1<46 1988 45 JAZ https://doi.org/10.1017/S1446788700032250 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700032250 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bloom Walter R. School of Mathematical and Physical Sciences Murdoch University Perth, Western Australia 6150, Australia NATIONALLICENCE 700 1- Fournier John J. F. Department of Mathematics University of British Columbia Vancouver, Canada V6T 1Y4 NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 45/1(1988-08), 46-61 1446-7887 45:1<46 1988 45 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge