Lebesgue Points of Besov and Triebel–Lizorkin Spaces with Generalized Smoothness
In this article, the authors study the Lebesgue point of functions from Hajłasz–Sobolev, Besov, and Triebel–Lizorkin spaces with generalized smoothness on doubling metric measure spaces and prove that the exceptional sets of their Lebesgue points have zero capacity via the capacities related to thes...
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| Auteurs principaux: | , , |
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| Format: | article |
| Langue: | EN |
| Publié: |
MDPI AG
2021
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| Sujets: | |
| Accès en ligne: | https://doaj.org/article/c2f09e2e19ef4920b1c8c2141be91e07 |
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| Résumé: | In this article, the authors study the Lebesgue point of functions from Hajłasz–Sobolev, Besov, and Triebel–Lizorkin spaces with generalized smoothness on doubling metric measure spaces and prove that the exceptional sets of their Lebesgue points have zero capacity via the capacities related to these spaces. In case these functions are not locally integrable, the authors also consider their generalized Lebesgue points defined via the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>-medians instead of the classical ball integral averages and establish the corresponding zero-capacity property of the exceptional sets. |
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