Dirichlet problem and Sokhotski-Plemelj jump formula on Weil-Petersson class quasidisks (Q2790811)

Let \(D^{+}:=\{z: |z|<1\}\), \(D^{-}:=\{z: |z|>1\}\). A one-to-one analytic mapping \(f: D^{+}\to {\mathbb C}\) is called a \(WP\)-mapping if it has a quasiconformal extension to \(\overline{\mathbb C}\) whose Beltrami coefficient \(\mu\) is square-integrable with respect to the hyperbolic area element on \(D^-\). The image of a \(WP\)-mapping is called a \(WP\)-quasidisk, and its boundary is called a \(WP\)-quasicircle.NEWLINENEWLINEThe authors show that any \(WP\)-quasicircle is a chord-arc curve, and prove the solvability of the Dirichlet problem for \(WP\)-quasidisks and the Sokhotski-Plemelj formula for \(WP\)-quasicircles.