Search results for "Hardyn avaruudet"

showing 2 items of 2 documents

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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Weighted Hardy Spaces of Quasiconformal Mappings

2019

We establish a weighted version of the $H^p$-theory of quasiconformal mappings.

radial maximal functionsfunktioteoriaHardy spacesMathematics - Complex Variablesmodulus estimateHardyn avaruudetFOS: Mathematicsquasiconformal mappingGeometry and TopologyComplex Variables (math.CV)nontangential30C65The Journal of Geometric Analysis
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