6533b838fe1ef96bd12a5017

RESEARCH PRODUCT

Hardy inequalities and Assouad dimensions

Juha Lehrbäck

subject

Pure mathematics26D15 (Primary) 31E05 46E35 (Secondary)Partial differential equationGeneral Mathematics010102 general mathematicsDuality (mathematics)01 natural sciencesFunctional Analysis (math.FA)010101 applied mathematicsMathematics - Functional AnalysisMetric spaceAssouad (co)dimensionsMathematics - Classical Analysis and ODEsEuclidean geometryClassical Analysis and ODEs (math.CA)FOS: Mathematicsmetric spaces Hardy inequalities0101 mathematicsAnalysisMathematicsComplement (set theory)

description

We establish both sufficient and necessary conditions for weighted Hardy inequalities in metric spaces in terms of Assouad (co)dimensions. Our sufficient conditions in the case where the complement is thin are new even in Euclidean spaces, while in the case of a thick complement we give new formulations for previously known sufficient conditions which reveal a natural duality between these two cases. Our necessary conditions are rather straight-forward generalizations from the unweighted case, but together with some examples they indicate the essential sharpness of our results. In addition, we consider the mixed case where the complement may contain both thick and thin parts.

yearjournalcountryeditionlanguage
2017-03-01
http://urn.fi/URN:NBN:fi:jyu-201906253430