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ORLICZ-POINCARE INEQUALITIES AND EMBEDDINGS OF ORLICZ-SOBOLEV SPACES ON METRIC SPACES


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

Issue:

SSRSMI, Number 1, Volume XX

Section:

Volume 20, Number 1

Abstract:

The main result of this paper shows that an Orlicz-Sobolev space with zero boundary values on a doubling metric measure space with homogeneous dimension s, corresponding to an Orlicz function generalizing tq with q < s, is continuously embedded in an Orlicz space generalizing Lq*, where q* = sq/(s-q). In order to prove this embedding result, we use an optimal result of Heikkinen [18] describing sharp self-improving properties of Orlicz-Poincare inequalities in connected metric spaces. We also prove an Orlicz-Poincare inequality for functions vanishing on large subsets of balls and some counterparts of the results mentioned above for Orlicz-Sobolev spaces of Hajlasz type.

Keywords:

metric measure space, Orlicz-Sobolev space, Orlicz-Sobolev space with zero boundary values, Poincare inequality, continuous embedding.

Code [ID]:

SSRSMI201001V20S01A0012 [0003177]

Full paper:

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