Dirichlet problem and sokhotski-plemelj jump formula on weil-petersson class quasidisks

David Radnell, Eric Schippers, Wolfgang Staubach

Research output: Contribution to journalArticleScientificpeer-review

6 Citations (Scopus)

Abstract

We show the solvability of the Dirichlet problem on Weil-Petersson class quasidisks and establish a Sokhotski-Plemelj jump formula for Weil-Petersson class quasicircles. Furthermore we show that the resulting Cauchy projections are bounded. In both cases the boundary data belongs to a certain conformally invariant Besov space. Moreover we show that the WP-class quasicircles are chord-arc curves.

Original languageEnglish
Pages (from-to)119-127
Number of pages9
JournalANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA
Volume41
Issue number1
DOIs
Publication statusPublished - 2016
MoE publication typeA1 Journal article-refereed

Keywords

  • Besov spaces
  • Cauchy integral
  • Chord-arc curves
  • Dirichlet problem
  • Poincaré inequality
  • Quasicircles
  • Quasiconformal extension
  • Sokhotski-plemelj jump decomposition
  • Weil-petersson class

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