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Dirichlet's problem and Sokhotski-Plemelj's jump formula on Weil-Petersson-Class quasidisks
Aalto Univ, Dept Math & Syst Anal, POB 11100, FI-00076 Aalto, Finland.
Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2016 (English)In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 41, no 1, 119-127 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2016. Vol. 41, no 1, 119-127 p.
Keyword [en]
Dirichlet problem; quasicircles; quasiconformal extension; Poincare inequality; chord-arc curves; Sokhotski-Plemelj jump decomposition; Cauchy integral; Besov spaces; Weil-Petersson class
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-285984DOI: 10.5186/aasfm.2016.4108ISI: 000371365600008OAI: oai:DiVA.org:uu-285984DiVA: diva2:921399
Available from: 2016-04-20 Created: 2016-04-20 Last updated: 2017-11-30Bibliographically approved

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