Search results for " 30L05"

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Dyadic Norm Besov-Type Spaces as Trace Spaces on Regular Trees

2019

In this paper, we study function spaces defined via dyadic energies on the boundaries of regular trees. We show that correct choices of dyadic energies result in Besov-type spaces that are trace spaces of (weighted) first order Sobolev spaces.

Pure mathematicsFunction spacetrace spaceMathematics::Analysis of PDEsMathematics::Classical Analysis and ODEs01 natural sciencesPotential theoryfunktioteoriaregular treeFOS: Mathematicsdyadic norm0101 mathematicsMathematics46E35 30L05Mathematics::Functional Analysis010102 general mathematicsFirst orderFunctional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicsSobolev spaceNorm (mathematics)Besov-type spacepotentiaaliteoriafunktionaalianalyysiAnalysisPotential Analysis
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Geometry and quasisymmetric parametrization of Semmes spaces

2011

We consider decomposition spaces R 3 /G that are manifold factors and admit defining sequences consisting of cubes-with-handles of finite type. Metrics on R 3 /G constructed via modular embeddings of R 3 /G into a Euclidean space promote the controlled topology to a controlled geometry. The quasisymmetric parametrizability of the metric space R 3 /G×R m by R 3+m for any m ≥ 0 imposes quantitative topological constraints, in terms of the circulation and the growth of the cubes-with-handles, on the defining sequences for R 3 /G. We give a necessary condition and a sufficient condition for the existence of such a parametrization. The necessary condition answers negatively a question of Heinone…

decomposition spaceMathematics - Geometric TopologyquasispherequasisymmetryMathematics - Metric GeometryFOS: Mathematics30L10 30L05 30C65parametrizationMetric Geometry (math.MG)Geometric Topology (math.GT)
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