Reverse Triangle Inequalities for Riesz Potentials and Connections with Polarization

TL;DR

This paper explores reverse triangle inequalities for Riesz potentials, linking them to polarization, and generalizes existing inequalities for polynomial norms and logarithmic potentials using potential theory techniques.

Contribution

It introduces a generalization of inequalities for Riesz potentials and connects these to polarization, expanding the theoretical framework of potential inequalities.

Findings

Established new reverse triangle inequalities for Riesz potentials

Connected inequalities with polarization concepts

Extended inequalities for polynomial sup norms and logarithmic potentials

Abstract

We study reverse triangle inequalities for Riesz potentials and their connection with polarization. This work generalizes inequalities for sup norms of products of polynomials, and reverse triangle inequalities for logarithmic potentials. The main tool used in the proofs is the representation for a power of the farthest distance function as a Riesz potential of a unit Borel measure.