Sharp Hardy type inequalities with weights depending on bessel function

Abstract

© Nasibullin R.G. 2017. We prove exact Hardy type inequalities with the weights depending on a Bessel function. We obtain one-dimensional L p -inequalities and provide an example of extending these inequalities for the case of convex domains with a finite inner radius. The proved statements are generalization for the case of arbitrary p ≥ 2 of the corresponding inequality proved by F.G. Avkhadiev and K.-J. Wirths for p = 2.