Weighted estimates for diffeomorphic extensions of homeomorphisms

Haiqing Xu

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arXiv · 1905.09330

Weighted estimates for diffeomorphic extensions of homeomorphisms

Haiqing Xu

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Abstract

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

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Haiqing Xu. 2019-05-22. Weighted estimates for diffeomorphic extensions of homeomorphisms. https://arxiv.org/abs/1905.09330

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