# Weighted estimates for diffeomorphic extensions of homeomorphisms

### Haiqing Xu

University of Jyväskylä, Finland and University of Science and Technology of China, Hefei, China

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## Abstract

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 $\varphi^{-1}$.

## Cite this article

Haiqing Xu, Weighted estimates for diffeomorphic extensions of homeomorphisms. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 31 (2020), no. 1, pp. 151–189

DOI 10.4171/RLM/884