Inequalities and Asymptotics for some Moment Integrals

2017/04/26 by Abi-Khuzam, Faruk
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1704.08144

Abstract

For α>β-1>0, we obtain two sided inequalities for the moment integral I(α,β)= ∫_ℝ |x|^-β|sin x|^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.

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