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RESEARCH PRODUCT

Self-improvement of weighted pointwise inequalities on open sets

Sylvester Eriksson-biqueAntti V. VähäkangasJuha Lehrbäck

subject

Pure mathematicsPrimary 35A23 Secondary 42B25 31E05Inequalitymedia_common.quotation_subjectMathematics::Classical Analysis and ODEsOpen setSpace (mathematics)Measure (mathematics)Mathematics - Analysis of PDEsmetrinen avaruusClassical Analysis and ODEs (math.CA)FOS: Mathematicspointwise Hardy inequalitymedia_commonMathematicsPointwiseMathematics::Functional AnalysisSelf improvementmetric spaceweightConnection (mathematics)Hardyn epäyhtälöMathematics - Classical Analysis and ODEsself-improvementMetric (mathematics)maximal operatorAnalysisAnalysis of PDEs (math.AP)

description

We prove a general self-improvement property for a family of weighted pointwise inequalities on open sets, including pointwise Hardy inequalities with distance weights. For this purpose we introduce and study the classes of $p$-Poincar\'e and $p$-Hardy weights for an open set $\Omega\subset X$, where $X$ is a metric measure space. We also apply the self-improvement of weighted pointwise Hardy inequalities in connection with usual integral versions of Hardy inequalities.

yearjournalcountryeditionlanguage
2020-02-25Journal of Functional Analysis
https://doi.org/10.1016/j.jfa.2020.108691