Mathematical Research Letters

Volume 15 (2008)

Number 4

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

Pages: 779 – 793

DOI: http://dx.doi.org/10.4310/MRL.2008.v15.n4.a14

Authors

Albert Clop (Universitat Autònoma de Barcelona)

Xavier Tolsa (University of Jyväskylä)

Abstract

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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