Dirichlet problem and Sokhotski-Plemelj jump formula on Weil-Petersson class quasidisks

David Radnell, Eric Schippers, Wolfgang Staubach
2016 Annales Academiae Scientiarum Fennicae: Mathematica  
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.
doi:10.5186/aasfm.2016.4108 fatcat:bnumrjtvvzaajht3c5ghkggn64