Search results for "31C05"

showing 2 items of 2 documents

Classification criteria for regular trees

2021

Esitämme säännöllisten puiden parabolisuudelle yhtäpitäviä ehtoja. We give characterizations for the parabolicity of regular trees. peerReviewed

Regular treeCapacityparabolicitycapacity31C05 31C15 31C45 31E05Mathematics::Analysis of PDEsMetric Geometry (math.MG)ArticlesFunctional Analysis (math.FA)CombinatoricsMathematics - Functional AnalysisfunktioanalyysiMathematics - Analysis of PDEsregular treeHarmonic functionMathematics - Metric Geometryharmonic functionFOS: MathematicsMathematicsAnalysis of PDEs (math.AP)
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Riesz transform and vertical oscillation in the Heisenberg group

2023

We study the $L^{2}$-boundedness of the $3$-dimensional (Heisenberg) Riesz transform on intrinsic Lipschitz graphs in the first Heisenberg group $\mathbb{H}$. Inspired by the notion of vertical perimeter, recently defined and studied by Lafforgue, Naor, and Young, we first introduce new scale and translation invariant coefficients $\operatorname{osc}_{\Omega}(B(q,r))$. These coefficients quantify the vertical oscillation of a domain $\Omega \subset \mathbb{H}$ around a point $q \in \partial \Omega$, at scale $r > 0$. We then proceed to show that if $\Omega$ is a domain bounded by an intrinsic Lipschitz graph $\Gamma$, and $$\int_{0}^{\infty} \operatorname{osc}_{\Omega}(B(q,r)) \, \frac{dr}{…

Riesz transformNumerical Analysisintrinsic Lipschitz graphsApplied MathematicsHeisenberg groupFunctional Analysis (math.FA)Mathematics - Functional Analysis42B20 (Primary) 31C05 35R03 32U30 28A78 (Secondary)Mathematics - Classical Analysis and ODEsClassical Analysis and ODEs (math.CA)FOS: MathematicsMathematics::Metric Geometrysingular integralsAnalysis
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