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Journal of the London Mathematical Society 1988 s2-37(121):105-118; doi:10.1112/jlms/s2-37.121.105
© 1988 by London Mathematical Society
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© The London Mathematical Society

prod-Variation with Remainder

E. Omey and E. Willekens

Economische Hogeschool Sint-Aloysius Broekstraat 113, 1000 Brussel, Belgium
Kath. Universiteit Leuven, Dept. Wiskunde Celestijnenlaan 200 B, 3030 Leuven, Belgium

Received 30 November 1985. Revision received 23 June 1986. Revision received 26 February 1987.

Let b: R+ -> R+ be an O-regularly varying function. In this paper we are concerned with the class of functions L for which there exists a function a: R+ -> R such that L(tx) – L(x) – a(x) log(t) = O(b(x)) as x -> {infty} for t > 0. We also discuss Abel-Tauber-Mercer theorems for a class of integral transforms of these functions.


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