6533b855fe1ef96bd12b0a06

RESEARCH PRODUCT

A maximal Function Approach to Two-Measure Poincaré Inequalities

Antti V. VähäkangasJuha KinnunenJuha LehrbäckRiikka Korte

subject

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

description

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 the assumptions. Harmonic analysis and PDE techniques are used extensively in the arguments.

yearjournalcountryeditionlanguage
2018-07-18
http://urn.fi/URN:NBN:fi:jyu-201906253435