Open Access
2011 Homogeneous Subsets of a Lipschitz Graph and the Corona Theorem
Brady Max NewDelman
Publ. Mat. 55(1): 93-121 (2011).


This paper proves the Corona Theorem to be affirmative for domains in the complex plane bounded by thick subsets of a Lipschitz graph. Specifically, the boundary of these domains $E_0$ has a Carleson lower density:

$$ \Lambda\left(B(z,r) \cap E_0\right) > \epsilon_0 r \quad\text{for all } z\in E_0, \quad \text{and all } r>0. $$


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Brady Max NewDelman. "Homogeneous Subsets of a Lipschitz Graph and the Corona Theorem." Publ. Mat. 55 (1) 93 - 121, 2011.


Published: 2011
First available in Project Euclid: 25 February 2011

zbMATH: 1217.30023
MathSciNet: MR2779577

Primary: 30-XX

Keywords: Corona , harmonic , homogeneous , Lipschitz , measure

Rights: Copyright © 2011 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.55 • No. 1 • 2011
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