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Sibirskii Matematicheskii Zhurnal, 2015, Volume 56, Number 5, Pages 1030–1036
DOI: https://doi.org/10.17377/smzh.2015.56.504 (Mi smj2694) 		 
Generalized Hajłasz–Sobolev classes on ultrametric measure spaces with doubling condition

E. V. Gubkinaa, M. A. Prokhorovichb, Ya. M. Radynab

a Gorno-Altaisk State University, Gorno-Altaisk, Russia
b Belarusian State University, Faculty of Mathematics and Mechanics, Minsk, Belarus
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DOI: https://doi.org/10.17377/smzh.2015.56.504
Abstract: We consider the generalized Hajłasz–Sobolev classes Wpα(X), α>0, on ultrametric measure spaces X with doubling condition. We study the massiveness of the complement to the set of Lebesgue points, the convergence rate for Steklov averages, and the problem of Luzin approximation. Bounds for the sizes of exceptional sets are given in terms of capacities.
It is substantial that we remove the constraint α⩽1 that is necessary for metric spaces. The results of the article were announced in Dokl. Nats. Akad. Nauk Belarusi.
Keywords: Lebesgue point, convergence rate for Steklov averages, Luzin approximation, Hajłasz–Sobolev class, capacity.
Received: 08.01.2015
Revised: 19.02.2015
English version:
Siberian Mathematical Journal, 2015, Volume 56, Issue 5, Pages 822–826
DOI: https://doi.org/10.1134/S0037446615050043
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: E. V. Gubkina, M. A. Prokhorovich, Ya. M. Radyna, “Generalized Hajłasz–Sobolev classes on ultrametric measure spaces with doubling condition”, Sibirsk. Mat. Zh., 56:5 (2015), 1030–1036; Siberian Math. J., 56:5 (2015), 822–826
Citation in format AMSBIB
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