Optimal Hardy inequalities associated with multipolar Schr\"odinger operators

TL;DR

This paper establishes optimal Hardy inequalities related to multipolar Schrödinger operators, deriving sharp constants and improved inequalities that have implications for multipolar Heisenberg inequalities and spectral analysis.

Contribution

It introduces new optimal Hardy inequalities for multipolar Schrödinger operators, including sharp constants and improved bounds on bounded domains.

Findings

Derived optimal Hardy inequalities with sharp constants.

Established improved multipolar Hardy inequalities on bounded domains.

Determined the range of the best Hardy constant for specific inequalities.

Abstract

We proved some optimal Hardy inequalities in RNwhich is closely related to multipolar Schr\"odinger operators with mean-value type potentials, these sharp inequalities imply some multipolar type Heisenberg inequalities. We also obtained someimproved multipolar Hardy inequalities on bounded domains, moreover, we got the range of the best Hardy constant for a specific Hardy inequality.