Smoothness conditions and integrability theorems on bounded Vilenkin groups

Journal of the Australian Mathematical Society

Walter R. Bloom¹ 

[1] John J. F. Fournier

关键词: primary 42 C 10;    secondary 43 A 50;    43 A 70;   

DOI  :  10.1017/S1446788700032250

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

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.

【 授权许可】

Unknown