Hausdorff dimension of Lebesgue sets for \(W \alpha p\) classes on metric spaces

DOI10.1134/S0001434607070115zbMath1220.46023MaRDI QIDQ635540

M. A. Prokhorovich

Publication date: 20 August 2011

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

Sobolev spacecapacitymetric spaceHausdorff dimensionSobolev classBorel measureLebesgue set

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Hausdorff and packing measures (28A78)

Related Items (5)

Approximation and quasicontinuity of Besov and Triebel–Lizorkin functions ⋮ Generalized Lebesgue points for Hajłasz functions ⋮ Fine properties of functions from Hajłasz-Sobolev classes \(M_\alpha^p\), \(p > 0\). I: Lebesgue points ⋮ Generalized Hajłasz-Sobolev classes on ultrametric measure spaces with doubling condition ⋮ Hausdorff measures and Lebesgue points for the Sobolev classes \(W_{\alpha }^p\), \(\alpha > 0\), on spaces of homogeneous type

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• New characterizations of Hajłasz-Sobolev spaces on metric spaces
• Compactness of embeddings of Sobolev type on metric measure spaces
• Hölder quasicontinuity of Sobolev functions on metric spaces
• Lebesgue points for Sobolev functions on metric spaces.
• Lectures on analysis on metric spaces
• A note on Hajłasz-Sobolev spaces on fractals
• Generalized Sobolev classes on metric measure spaces
• Analyse harmonique non-commutative sur certains espaces homogènes. Etude de certaines intégrales singulières. (Non-commutative harmonic analysis on certain homogeneous spaces. Study of certain singular integrals.)
• Pointwise Differentiability and Absolute Continuity
• Extensions of Hardy spaces and their use in analysis

This page was built for publication: Hausdorff dimension of Lebesgue sets for \(W \alpha p\) classes on metric spaces