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

• Autores: Albert Clop , Xavier Tolsa Domènech
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 15, Nº 4, 2008, págs. 779-793
• Idioma: inglés
• DOI: 10.4310/mrl.2008.v15.n4.a14
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• Resumen

  • 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 $W^{1,2}$.