Generalized Hajłasz-Sobolev classes on ultrametric measure spaces with doubling condition

DOI10.1134/S0037446615050043zbMath1350.46026MaRDI QIDQ5963436

M. A. Prokhorovich, Ya. M. Radyna, E. V. Gubkina

Publication date: 19 February 2016

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

Full work available at URL: http://mathnet.ru/eng/smj2694

zbMATH Keywords

capacityLebesgue pointconvergence rate for Steklov averagesHajłasz-Sobolev classLuzin approximation

Mathematics Subject Classification ID

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

Cites Work

• Hausdorff dimension of Lebesgue sets for \(W \alpha p\) classes on metric spaces
• The rate of convergence of Steklov means on metric measure spaces and Hausdorff dimension
• The Luzin approximation of functions from classes \(W_\alpha ^p\) on metric spaces with measure
• Hausdorff measures and Lebesgue points for the Sobolev classes \(W_{\alpha }^p\), \(\alpha > 0\), on spaces of homogeneous type
• Biorthogonal wavelets on Vilenkin groups
• 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.
• Embedding theorems for generalized Sobolev spaces
• Lectures on analysis on metric spaces
• Sobolev spaces on an arbitrary metric space
• Colloquium lectures on geometric measure theory
• Estimates for singular integral operators in terms of maximal functions
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