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DENSE SUBCLASSES IN ABSTRACT SOBOLEV SPACES ON METRIC MEASURE SPACES


MARCELINA MOCANU
Department of Mathematics and Informatics, Faculty of Sciences, “Vasile
Alecsandri" University of Bacău, Calea Mărăşeşti 157, Bacău 600115,
ROMANIA,
e-mail: mmocanu@ub.ro

Issue:

SSRSMI, Number 2, Volume XXII

Section:

Volume 22, Number 2

Abstract:

Given a metric measure space (X; d; μ) and a Banach function space B over X that has absolutely continuous norm, we prove two results regarding the density in the Newtonian space N^ 1,B (X) of the subclasses consisting of bounded functions, respectively of bounded functions supported in closed balls. We do not assume that μ is a doubling measure. If B is rearrangement invariant, (X; d) is proper and the measure μ is non-atomic, it turns out that the class of bounded compactly supported functions from

N^ 1,B (X) is dense in N^ 1,B (X).

Keywords:

metric measure space, Banach function space, (generalized) weak upper gradient, Newtonian space.

Code [ID]:

SSRSMI20120222V22S01A0007 [0003800]

Full paper:

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