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Sibirsk. Mat. Zh., 2015, Volume 56, Number 5, Pages 1030–1036 (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

Abstract: We consider the generalized Hajłasz–Sobolev classes $W^p_\alpha (X)$, $\alpha>0$, 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 $\alpha\le1$ 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.

DOI: https://doi.org/10.17377/smzh.2015.56.504

Full text: PDF file (280 kB)
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English version:
Siberian Mathematical Journal, 2015, 56:5, 822–826

Bibliographic databases:

UDC: 517.5
Received: 08.01.2015
Revised: 19.02.2015

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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\paper Generalized Haj\l asz--Sobolev classes on ultrametric measure spaces with doubling condition
\jour Sibirsk. Mat. Zh.
\yr 2015
\vol 56
\issue 5
\pages 1030--1036
\mathnet{http://mi.mathnet.ru/smj2694}
\crossref{https://doi.org/10.17377/smzh.2015.56.504}
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\jour Siberian Math. J.
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\vol 56
\issue 5
\pages 822--826
\crossref{https://doi.org/10.1134/S0037446615050043}
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