Fractional Poincaré and localized Hardy inequalities on metric spaces

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 c...

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Bibliographic Details
Published inAdvances in calculus of variations Vol. 16; no. 4; pp. 867 - 884
Main Authors Dyda, Bartłomiej, Lehrbäck, Juha, Vähäkangas, Antti V.
Format Journal Article
LanguageEnglish
Published Berlin De Gruyter 01.10.2023
Walter de Gruyter GmbH
Subjects
26D15
31C15
35A23
fractional Hardy inequality
Fractional Poincaré inequality
Inequalities
metric measure space
Metric space
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Summary: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.
ISSN:1864-8258
1864-8266
DOI:10.1515/acv-2021-0069