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Homogeneous Subsets of a Lipschitz Graph and the Corona Theorem

Brady Max NewDelman

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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

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

First available in Project Euclid: 25 February 2011

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 30-XX: FUNCTIONS OF A COMPLEX VARIABLE {For analysis on manifolds, see 58-XX}

Corona harmonic measure homogeneous Lipschitz


NewDelman, Brady Max. Homogeneous Subsets of a Lipschitz Graph and the Corona Theorem. Publ. Mat. 55 (2011), no. 1, 93--121.

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