On a reverse Hölder inequality for Schrödinger operators

Abstract

We obtain a reverse Hölder inequality for the eigenfuctions of the Schrödinger operator with slowly decaying potentials. The class of potentials includes singular potentials which decay like $|x{|}^{-\alpha }$ with $0<\alpha <2$, in particular the Coulomb potential.

arXiv commentTo appear in Arch. Math., 9 pages, two dimensional result added