Inequalities for sums of Green potentials and Blaschke products

TL;DR

This paper establishes new inequalities involving Green potentials on compact sets in the complex plane and applies these results to derive sharp bounds for the supremum norms of Blaschke products.

Contribution

It introduces a novel representation of the pseudohyperbolic farthest-point distance function using Green potentials, advancing the theoretical framework for potential inequalities.

Findings

Derived inequalities for Green potentials on compact sets

Provided new representation of pseudohyperbolic distance via Green potentials

Established sharp bounds for supremum norms of Blaschke products

Abstract

We study inequalities for the infima of Green potentials on a compact subset of an arbitrary domain in the complex plane. The results are based on a new representation of the pseudohyperbolic farthest-point distance function via a Green potential. We also give applications to sharp inequalities for the supremum norms of Blaschke products.