6533b7d6fe1ef96bd1267061

RESEARCH PRODUCT

Assouad Type Dimensions in Geometric Analysis

Juha Lehrbäck

subject

osittaisdifferentiaaliyhtälötPure mathematicsLower dimensionGeometric analysisAssouad dimensionAikawa conditionHardy–Sobolev inequalityDimension (graph theory)Hausdorff spaceMuckenhoupt weightCharacterization (mathematics)Type (model theory)Dual (category theory)Content (measure theory)Mathematics::Metric GeometrymittateoriaepäyhtälötMathematicsDual pair

description

We consider applications of the dual pair of the (upper) Assouad dimension and the lower (Assouad) dimension in analysis. We relate these notions to other dimensional conditions such as a Hausdorff content density condition and an integrability condition for the distance function. The latter condition leads to a characterization of the Muckenhoupt Ap properties of distance functions in terms of the (upper) Assouad dimension. It is also possible to give natural formulations for the validity of Hardy–Sobolev inequalities using these dual Assouad dimensions, and this helps to understand the previously observed dual nature of certain cases of these inequalities. peerReviewed

yearjournalcountryeditionlanguage
2021-01-01
https://doi.org/10.1007/978-3-030-59649-1_2