Reverse Triangle Inequalities for Riesz Potentials and Connections with Polarization

2013/07/23 by Igor E. Pritsker, Edward B. Saff, Pritsker, I. E. +3
Mathematics · #30C15 #52A40 #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical functions and polynomials #Primary 31A15 #Secondary 31A05

paper · pdf · doi:10.48550/arxiv.1307.6205

openalex publication_date 2013/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Riesz Polarization Inequalities in Higher Dimensions
• Pointwise estimates to the modified Riesz potential
• Reverse Faber-Krahn inequalities for the Logarithmic potential operator
• Riesz potential estimates under co-canceling constraints
• Optimal weak estimates for Riesz potentials