Inequalities for real powers of completely monotonic functions
Further improvements of the author's results from the previous paper [J. Math. Anal. Appl. 204, No. 2, 389-408 (1996; preceding review)] are obtained. Namely, the implication \[ f\in L\Rightarrow [\forall \alpha> 1: f^\alpha\in L^N] \] is true for \(0\leq N\leq 7\), but false for \(N\geq 13\). Some inequalities for completely monotonic functions are also obtained.
scientific article; zbMATH DE number 1031638