6533b824fe1ef96bd1280066

RESEARCH PRODUCT

Weighted estimates for diffeomorphic extensions of homeomorphisms

Haiqing Xu

subject

Pure mathematicsMathematics::Functional AnalysisMathematics - Complex VariablesdiffeomorphismGeneral MathematicsMultiple integralHigh Energy Physics::Phenomenologyinternal chord-arc domainPoisson extensionExtension (predicate logic)OmegafunktioteoriaHomeomorphism (graph theory)Domain (ring theory)FOS: MathematicsDiffeomorphismComplex Variables (math.CV)Mathematics

description

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 $\varphi^{-1} .$

yearjournalcountryeditionlanguage
2019-05-22
http://arxiv.org/abs/1905.09330