Fractional Poincaré and localized Hardy inequalities on metric spaces

2021/08/16 by Bartłomiej Dyda, Dyda, Bartłomiej, Juha Lehrbäck +3 · 2 citations
Mathematics · #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.2108.07209

Abstract

We prove fractional Sobolev-Poincaré inequalities, capacitary versions of fractional Poincaré inequalities, and pointwise and localized fractional Hardy inequalities in a metric space equipped with a doubling measure. Our results generalize and extend earlier work where such inequalities have been considered in the Euclidean spaces or in the non-fractional setting in metric spaces. The results concerning pointwise and localized variants of fractional Hardy inequalities are new even in the Euclidean case.

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