Fine properties of functions from Hajłasz-Sobolev classes \(M_\alpha^p\), \(p > 0\). II: Lusin's approximation

DOI10.3103/S1068362317010046zbMath1458.46026OpenAlexW2736209148MaRDI QIDQ528882

V. G. Krotov, S. A. Bondarev

Publication date: 17 May 2017

Published in: Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s1068362317010046

zbMATH Keywords

Sobolev spacecapacityouter measuremetric measure spacedoubling conditionHausdorff measure and dimensionLusin's approximation

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Special properties of functions of several variables, Hölder conditions, etc. (26B35) Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces (46E36)

Related Items (1)

On the continuity of best approximations by constants on balls in metric measure spaces

Cites Work

• Fine properties of functions from Hajłasz-Sobolev classes \(M_\alpha^p\), \(p > 0\). I: Lebesgue points
• The rate of convergence of Steklov means on metric measure spaces and Hausdorff dimension
• Approximation by Hölder functions in Besov and Triebel-Lizorkin spaces
• A decomposition into atoms of distributions on spaces of homogeneous type
• Hölder quasicontinuity of Sobolev functions on metric spaces
• Lebesgue points for Sobolev functions on metric spaces.
• Sobolev spaces on an arbitrary metric space
• Estimates of \(L^p\)-oscillations of functions for \(p>0\)
• Pointwise behaviour of \(M^{1,1}\) Sobolev functions

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