# Article

Ufa Mathematical Journal
Volume 9, Number 1, pp. 89-97

# Sharp Hardy type inequalities with weights depending on Bessel function

Nasibullin R.G.

DOI:10.13108/2017-9-1-89

We obtain a new sharp Hardy type inequality with weights. Using the Bessel functions we prove Lp one dimensional inequality and their multidimensional analogs in convex domains. The weight functions depend on the Bessel functions and LambвЂ™s constants. 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 $p\geqslant 2$ of the corresponding inequality proved by F.G. Avkhadiev and K.-J. Wirths for $p=2$.