Weighted estimates for diffeomorphic extensions of homeomorphisms

Abstract

Let $Ω\subset \mbr^2$ be an internal chord-arc domain and $φ: \mbs^1 \rightarrow \partial Ω$ be a homeomorphism. Then there is a diffeomorphic extension $h : \mbd \rightarrow Ω$ of $\phi .$ We study the relationship between weighted integrability of the derivatives of $h$ and double integrals of $\phi$ and of ${\phi }^{-1}.$