Inequalities and asymptotics for some moment integrals

Abstract

For α> β− 1 > 0 , we obtain two-sided inequalities for the moment integral I(=∫R|x|−β|sinx|αdx. These are then used to give the exact asymptotic behavior of the integral as α→ ∞. The case I(α, α) corresponds to the asymptotics of Ball’s inequality, and I(α, [α] − 1) corresponds to a kind of novel “oscillatory” behavior. © 2017, The Author(s).