TY - JOUR
T1 - Dirichlet problem and sokhotski-plemelj jump formula on weil-petersson class quasidisks
AU - Radnell, David
AU - Schippers, Eric
AU - Staubach, Wolfgang
PY - 2016
Y1 - 2016
N2 - 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.
AB - 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.
KW - Besov spaces
KW - Cauchy integral
KW - Chord-arc curves
KW - Dirichlet problem
KW - PoincarĂ© inequality
KW - Quasicircles
KW - Quasiconformal extension
KW - Sokhotski-plemelj jump decomposition
KW - Weil-petersson class
UR - http://www.scopus.com/inward/record.url?scp=84958765774&partnerID=8YFLogxK
U2 - 10.5186/aasfm.2016.4108
DO - 10.5186/aasfm.2016.4108
M3 - Article
VL - 41
SP - 119
EP - 127
JO - ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA
JF - ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA
SN - 1239-629X
IS - 1
ER -