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AN EXTENSION OF CHEEGER DIFFERENTIAL OPERATOR FROM LIPSCHITZ FUNCTIONS TO ORLICZ-SOBOLEV FUNCTIONS ON METRIC MEASURE SPACES


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

Issue:

SSRSMI, Number 1, Volume XXV

Section:

Volume 25, Number 1

Abstract:

We introduce two types of Orlicz-Sobolev spaces on a metric measure space. One space is the completion of locally Lipschitz functions in a norm of Orlicz-Sobolev type involving an abstract differentiation operator and the other space is de_ned via an Orlicz-PoincarĂ© inequality. We prove that these spaces agree and are reflexive provided that the measure is doubling and the Young function defining the underlying Orlicz space is doubling, together with its complementary function. In the case where the Young func-tion is a power function with exponent greater than one, we recover some results of Fran-chi, HajƂasz and Koskela (1999).

Keywords:

doubling metric measure space, Poincaré inequality, Orlicz-Sobolev space, strong measurable differentiable structure, Cheeger differential.

Code [ID]:

SSRSMI201501V25S01A0003 [0004212]

DOI:

Full paper:

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