Hausdorff measures and Lebesgue points for the Sobolev classes \(W_{\alpha }^p\), \(\alpha > 0\), on spaces of homogeneous type

DOI10.1134/S0001434609030298zbMath1182.46023MaRDI QIDQ1033965

M. A. Prokhorovich

Publication date: 10 November 2009

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

zbMATH Keywords

Hausdorff dimensionHausdorff measureBorel measureLebesgue pointHausdorff capacityHölder classes \(H^{\alpha }(X)\)Sobolev classes \(W_{\alpha }^p\)

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Length, area, volume, other geometric measure theory (28A75) Analysis on metric spaces (30L99)

Related Items (3)

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 ⋮ Maximal Functions Measuring Smoothness

Cites Work

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• Hausdorff dimension of Lebesgue sets for \(W \alpha p\) classes on metric spaces
• New characterizations of Hajłasz-Sobolev spaces on metric spaces
• Hölder quasicontinuity of Sobolev functions on metric spaces
• Lebesgue points for Sobolev functions on metric spaces.
• Haar wavelets of higher order on fractals and regularity of functions.
• Sobolev spaces on an arbitrary metric space
• Generalized Sobolev classes on metric measure spaces
• Extensions of Hardy spaces and their use in analysis
• Estimates for singular integral operators in terms of maximal functions

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