Search results for "kvasikonformikuvaukset"

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Hardy spaces and quasiconformal maps in the Heisenberg group

2023

We define Hardy spaces $H^p$, $00$ such that every $K$-quasiconformal map $f:B \to f(B) \subset \mathbb{H}^1$ belongs to $H^p$ for all $0<p<p_0(K)$. Second, we give two equivalent conditions for the $H^p$ membership of a quasiconformal map $f$, one in terms of the radial limits of $f$, and one using a nontangential maximal function of $f$. As an application, we characterize Carleson measures on $B$ via integral inequalities for quasiconformal mappings on $B$ and their radial limits. Our paper thus extends results by Astala and Koskela, Jerison and Weitsman, Nolder, and Zinsmeister, from $\mathbb{R}^n$ to $\mathbb{H}^1$. A crucial difference between the proofs in $\mathbb{R}^n$ and $\mathbb{…

Hardy spacesMathematics - Complex VariablesMetric Geometry (math.MG)quasiconformal mapsHeisenberg groupPrimary: 30L10 Secondary: 30C65 30H10Functional Analysis (math.FA)Mathematics - Functional AnalysiskvasikonformikuvauksetMathematics - Metric GeometryFOS: MathematicsHardyn avaruudetComplex Variables (math.CV)Carleson measuresAnalysis
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Bi-Sobolev extensions

2022

We give a full characterization of circle homeomorphisms which admit a homeomorphic extension to the unit disk with finite bi-Sobolev norm. As a special case, a bi-conformal variant of the famous Beurling-Ahlfors extension theorem is obtained. Furthermore we show that the existing extension techniques such as applying either the harmonic or the Beurling-Ahlfors operator work poorly in the degenerated setting. This also gives an affirmative answer to a question of Karafyllia and Ntalampekos.

Sobolev extensionskvasikonformikuvauksetMathematics - Complex VariablesPrimary 46E35 30C62. Secondary 58E20FOS: Mathematicsharmonic extensionquasiconformal mapping and mapping of finite distortionSobolev homeomorphismsComplex Variables (math.CV)Beurling-Ahlfors extension
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