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

Autor:	Ya. M. Radyna, M. A. Prokhorovich, E. V. Gubkina
Rok vydání:	2015
Předmět:	Discrete mathematics Pure mathematics General Mathematics Lebesgue integration Measure (mathematics) Sobolev space symbols.namesake Metric space Rate of convergence symbols Luzin N property Ultrametric space Mathematics Complement (set theory)
Zdroj:	Siberian Mathematical Journal. 56:822-826
ISSN:	1573-9260 0037-4466
Popis:	We consider the generalized Hajlasz–Sobolev classes W (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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::fe13cb96e29014e33b518c1e1e458a36 https://doi.org/10.1134/s0037446615050043 Zobrazit plný text záznamu Plný text ve formátu PDF