In metric-measure spaces Sobolev embedding is equivalent to a lower bound for the measure

DOI10.1007/s11118-016-9605-7zbMath1381.46032OpenAlexW2555991684WikidataQ59608156 ScholiaQ59608156MaRDI QIDQ2014389

Przemysław Górka

Publication date: 11 August 2017

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11118-016-9605-7

zbMATH Keywords

Sobolev spacesSobolev inequalitiesmetric measure spaceslower bound for measure

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Analysis on metric spaces (30L99)

Related Items (9)

A Singular Moser-Trudinger Inequality on Metric Measure Space ⋮ Measure density and embeddings of Hajłasz-Besov and Hajłasz-Triebel-Lizorkin spaces ⋮ Embedding of fractional Sobolev spaces is equivalent to regularity of the measure ⋮ A note on metric-measure spaces supporting Poincaré inequalities ⋮ Sobolev embeddings for fractional Hajłasz-Sobolev spaces in the setting of rearrangement invariant spaces ⋮ Looking for compactness in Sobolev spaces on noncompact metric spaces ⋮ Relatively compact sets in variable-exponent Lebesgue spaces ⋮ Orlicz-Sobolev embeddings, extensions and Orlicz-Poincaré inequalities ⋮ Sobolev embedding for \(M^{1, p}\) spaces is equivalent to a lower bound of the measure

Cites Work

• Lectures on analysis on metric spaces
• Sobolev spaces on an arbitrary metric space
• Sobolev embeddings, extensions and measure density condition
• Sobolev met Poincaré
• Sobolev Spaces on Metric Measure Spaces
• Fractional Sobolev extension and imbedding
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