Abstract
Determination of the operator norm for the Laplace transformation, when operating on Lebesgue spaces, is a long unsolved problem. Recently Setterqvist gave an improved bound to that norm. This note shows how his result relates to a more general theorem, which also gives a related reverse inequality, and some other results of Hardy, Littlewood and Pólya.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Notes
1 We use the word transformation to avoid confusion with the transform norm .