Improved Hardy inequality with logarithmic term

Abstract

New Hardy type inequality with double singular kernel and with additional logarithmic term in a ball $B\subset {\mathbb{R}}^n$ is proved. As an application an estimate from below of the first eigenvalue for Dirichlet problem of p-Laplacian in a bounded domain $\Omega \subset {\mathbb{R}}^n$ is obtain.

8 pages