Maximal function estimates and self-improvement results for Poincaré inequalities

Maximal function estimates and self-improvement results for Poincaré inequalities

Our main result is an estimate for a sharp maximal function, which implies a Keith–Zhong type self-improvement property of Poincaré inequalities related to differentiable structures on metric measure spaces. As an application, we give structure independent representation for Sobolev norms and univer...

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Veröffentlicht in:Manuscripta mathematica 2019-01, Vol.158 (1-2), p.119-147
Hauptverfasser: Kinnunen, Juha, Lehrbäck, Juha, Vähäkangas, Antti V., Zhong, Xiao
Format: Artikel
Sprache:eng
Schlagworte:
Algebraic Geometry
Calculus of Variations and Optimal Control
Optimization
Geometry
Inequalities
Lie Groups
Mathematics
Mathematics and Statistics
Norms
Number Theory
Sobolev space
Topological Groups
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Zusammenfassung:Our main result is an estimate for a sharp maximal function, which implies a Keith–Zhong type self-improvement property of Poincaré inequalities related to differentiable structures on metric measure spaces. As an application, we give structure independent representation for Sobolev norms and universality results for Sobolev spaces.
ISSN:0025-2611
1432-1785
DOI:10.1007/s00229-018-1016-1