Homogeneous Subsets of a Lipschitz Graph and the Corona Theorem

TL;DR

This paper proves that the Corona Theorem holds for domains bounded by homogeneous subsets of Lipschitz graphs, extending the understanding of boundary conditions under which the theorem is valid.

Contribution

It establishes the validity of the Corona Theorem for a new class of domains defined by homogeneous subsets of Lipschitz graphs.

Findings

Corona Theorem is affirmative for these domains

Extends previous results to homogeneous Lipschitz boundary subsets

Provides new techniques for boundary analysis in complex domains

Abstract

For a domain bounded by homogeneous subsets of a Lipschitz graph, we show the Corona Theorem is affirmative.