Search results for "Self improvement"

showing 3 items of 3 documents

Self-improvement of pointwise Hardy inequality

2019

We prove the self-improvement of a pointwise p p -Hardy inequality. The proof relies on maximal function techniques and a characterization of the inequality by curves.

Pure mathematicsInequalityGeneral Mathematicsmedia_common.quotation_subjectCharacterization (mathematics)Mathematics - Analysis of PDEsuniform fatnessClassical Analysis and ODEs (math.CA)FOS: Mathematicsepäyhtälötpointwise Hardy inequalitymedia_commonMathematicsPointwiseosittaisdifferentiaaliyhtälötSelf improvementApplied Mathematicsmetric spacemetriset avaruudetMetric spaceMathematics - Classical Analysis and ODEsself-improvementMaximal functionpotentiaaliteoria31C15 (Primary) 31E05 35A23 (Secondary)Analysis of PDEs (math.AP)
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Self-improvement of weighted pointwise inequalities on open sets

2020

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.

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)Journal of Functional Analysis
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A maximal Function Approach to Two-Measure Poincaré Inequalities

2018

This paper extends the self-improvement result of Keith and Zhong in  Keith and Zhong (Ann. Math. 167(2):575–599, 2008) to the two-measure case. Our main result shows that a two-measure (p, p)-Poincare inequality for $$10$$ under a balance condition on the measures. The corresponding result for a maximal Poincare inequality is also considered. In this case the left-hand side in the Poincare inequality is replaced with an integral of a sharp maximal function and the results hold without a balance condition. Moreover, validity of maximal Poincare inequalities is used to characterize the self-improvement of two-measure Poincare inequalities. Examples are constructed to illustrate the role of t…

Pure mathematicsSelf improvementInequalitymedia_common.quotation_subject010102 general mathematicsPoincaré inequality01 natural sciencesMeasure (mathematics)symbols.namesakeDifferential geometryPoincaré inequality0103 physical sciencesPoincaré conjectureself-improvementsymbolsMaximal functionpotentiaaliteoria010307 mathematical physicsGeometry and Topology0101 mathematicsfunktionaalianalyysiepäyhtälötgeodesic two-measure spaceMathematicsmedia_common
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