DENSE SUBCLASSES IN ABSTRACT SOBOLEV SPACES ON METRIC MEASURE SPACES

MARCELINA MOCANU Department of Mathematics and Informatics, Faculty of Sciences, â€œVasile Alecsandri" University of BacÄƒu, Calea MÄƒrÄƒÅŸeÅŸti 157, BacÄƒu 600115, ROMANIA,
e-mail: mmocanu@ub.ro

Given a metric measure space (X; d; Î¼) 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 Î¼ is a doubling measure. If B is rearrangement invariant, (X; d) is proper and the measure Î¼ is non-atomic, it turns out that the class of bounded compactly supported functions from