Weighted estimates for diffeomorphic extensions of homeomorphisms (Q2180290)

Summary: Let \(\Omega \subset \mathbb{R}^2\) be an internal chord-arc domain and \(\varphi : \mathbb{S}^1 \rightarrow \partial \Omega\) be a homeomorphism. Then there is a diffeomorphic extension \(h : \mathbb{D} \rightarrow \Omega\) of \(\varphi \). We study the relationship between weighted integrability of the derivatives of \(h\) and double integrals of \(\varphi\) and of \(\varphi^{-1}\).