Lipschitzness of the Lempert and Green functions
Nikolai Nikolov, Peter Pflug, Pascal J. Thomas
TL;DR
This paper establishes precise boundary conditions under which the Lempert and Green functions exhibit Lipschitz continuity, enhancing understanding of their regularity properties in complex analysis.
Contribution
It provides necessary and sufficient boundary conditions for the Lipschitzness of the Lempert and Green functions, a novel characterization in complex analysis.
Findings
Identifies boundary behaviors that ensure Lipschitz continuity.
Provides a complete characterization of Lipschitzness conditions.
Enhances understanding of regularity properties of these functions.
Abstract
Necessary and sufficient conditions for Lipschitzness of the Lempert and Green functions are found in terms of their boundary behaviors.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Banach Space Theory · Analytic and geometric function theory