Embedding of fractional Sobolev spaces is equivalent to regularity of the measure

DOI10.4064/sm220304-2-7OpenAlexW4292180138MaRDI QIDQ5058625

Przemysław Górka, Artur Słabuszewski

Publication date: 21 December 2022

Published in: Studia Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/sm220304-2-7

zbMATH Keywords

Sobolev spacesmetric measure spacesfractional spaceslower Ahlfors regular

Mathematics Subject Classification ID

Analysis on metric spaces (30L99) Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces (46E36)

Cites Work

• Sobolev embedding for \(M^{1, p}\) spaces is equivalent to a lower bound of the measure
• Lectures on analysis on metric spaces
• In metric-measure spaces Sobolev embedding is equivalent to a lower bound for the measure
• Variable exponent Sobolev spaces and regularity of domains
• Sobolev embeddings, extensions and measure density condition
• Measure density and embeddings of Hajłasz-Besov and Hajłasz-Triebel-Lizorkin spaces
• Embedding theorems for Lipschitz and Lorentz spaces on lower Ahlfors regular sets
• Lower bound of measure and embeddings of Sobolev, Besov and Triebel–Lizorkin spaces
• From Sobolev inequality to doubling
• Fractional Sobolev extension and imbedding

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