From Sobolev Inequality to Doubling
Lyudmila Korobenko, Diego Maldonado, and Cristian Rios
TL;DR
This paper explores how a weak Sobolev inequality can lead to a doubling property of measures, linking functional inequalities with measure-theoretic geometric properties.
Contribution
It establishes a theoretical connection showing that weak Sobolev inequalities imply measure doubling, enhancing understanding of measure properties in analysis.
Findings
Weak Sobolev inequalities imply measure doubling
Theoretical link between functional inequalities and measure properties
Provides a framework for analyzing measure behavior in analysis
Abstract
In various analytical contexts, it is proved that a weak Sobolev inequality implies a doubling property for the underlying measure.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Harmonic Analysis Research · Geometric Analysis and Curvature Flows