Mathematical Research Letters

Volume 15, Issue 4, July 2008 pp. 779-793.

Analytic capacity and quasiconformal mappings with $W^{1,2}$ Beltrami coefficient

Authors: Albert Clop (1) and Xavier Tolsa (2)
Author institution: Universitat Autònoma de Barcelona (1) and University of Jyväskylä (2)

Summary: We show that if $\phi$ is a quasiconformal mapping with compactly supported Beltrami coefficient in the Sobolev space $W^{1,2}$, then $\phi$ preserves sets with vanishing analytic capacity. It then follows that a compact set $E$ is removable for bounded analytic functions if and only if it is removable for bounded quasiregular mappings with compactly supported Beltrami coefficient in $W^{1,2}$.

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