## Publicacions Matemàtiques

### Homogeneous Subsets of a Lipschitz Graph and the Corona Theorem

#### Abstract

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:

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

#### Article information

Source
Publ. Mat. Volume 55, Number 1 (2011), 93-121.

Dates
First available in Project Euclid: 25 February 2011

http://projecteuclid.org/euclid.pm/1298670085

Zentralblatt MATH identifier
05849329

Mathematical Reviews number (MathSciNet)
MR2779577

#### Citation

NewDelman, Brady Max. Homogeneous Subsets of a Lipschitz Graph and the Corona Theorem. Publicacions Matemàtiques 55 (2011), no. 1, 93--121. http://projecteuclid.org/euclid.pm/1298670085.

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