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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