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

Research output: Contribution to journalArticleScientificpeer-review

Details

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

Researchers

Research units

  • University of Manitoba
  • Uppsala University

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.

    Research areas

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

ID: 1657741