A Berezin-Li-Yau type inequality for the fractional Laplacian on a bounded domain

Abstract

An improvement to a Berezin-Li-Yau type inequality for $(-\Delta {)}^{\alpha /2}{|}_{\Omega },$ the fractional Laplacian operators restriced to a bounded domain $\Omega \subset {\mathbb{R}}^d$ for $\alpha \in (0,2],$ $d\ge 2,$ is proved.

arXiv commentThis paper has been withdrawn by the author due to a crucial change. See the updated file published in: Communications in Contemporary Mathematics, Vol. 15, No. 3, (1250048) (2013) with the new title "Estimates for the sums of eigenvalues of the fractional Laplacian on a bounded domain."