Analytic capacity and quasiconformal mappings with W1,2 Beltrami coefficient

Albert Clop, Xavier Tolsa

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

We show that if φ a quasiconformal mapping with compactly supported Beltrami coefficient in the Sobolev space W1,2, then φ 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 W1,2. © International Press 2008.
Original languageEnglish
Pages (from-to)779-793
JournalMathematical Research Letters
Volume15
Issue number4
DOIs
Publication statusPublished - 1 Jan 2008

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