JournalsrlmVol. 31, No. 1pp. 151–189

Weighted estimates for diffeomorphic extensions of homeomorphisms

  • Haiqing Xu

    University of Jyväskylä, Finland and University of Science and Technology of China, Hefei, China
Weighted estimates for diffeomorphic extensions of homeomorphisms cover
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Abstract

Let ΩR2\Omega \subset \mathbb R^2 be an internal chord-arc domain and φ:S1Ω\varphi : \mathbb S^1 \rightarrow \partial \Omega be a homeomorphism. Then there is a diffeomorphic extension h:DΩh : \mathbb D \rightarrow \Omega of φ\varphi. We study the relationship between weighted integrability of the derivatives of hh and double integrals of φ\varphi and of φ1\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