On a reverse H\"older inequality for Schr\"odinger operators

TL;DR

This paper establishes a reverse H"older inequality for eigenfunctions of Schr"odinger operators with certain slowly decaying and singular potentials, including Coulomb potentials, expanding understanding of their regularity properties.

Contribution

It introduces a reverse H"older inequality applicable to Schr"odinger eigenfunctions with a broad class of decaying and singular potentials, including Coulomb.

Findings

Reverse H"older inequality proven for eigenfunctions

Applicable to potentials decaying like |x|^{-eta} with 0<β<2

Includes Coulomb potential as a special case

Abstract

We obtain a reverse H\"older inequality for the eigenfuctions of the Schr\"odinger 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.