ON THE DENSITY OF LIPSCHITZ FUNCTIONS IN NEWTONIAN SPACES
MARCELINA MOCANU “Vasile Alecsandri” University of Bacău, Faculty of Sciences, Department of Mathematics and Informatics, 157 Calea Mărășești, Bacău 600115, ROMANIA
e-mail: mmocanu@ub.ro
Let E be a rearrangement invariant Banach function space over a metric measure space X, where the measure of X is doubling and X supports a (1, E)-Poincaré inequality. We pro-vide sufficient conditions for the local Hölder continuity of a representative of each func-tion in N1,E (X), using a quasiconcavity property of a certain power of the fundamental function of E. Using the properties of a non-centered maximal operator based on E, we give a simple proof for the density of Lipschitz functions in a Newtonian space N1,E (X), under the assumptions that E has an absolutely continuous norm and
its fundamental function satisfies a certain lower estimate.
