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
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.
