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 t<sup>q</sup> with q < s, is continuously embedded in an Orlicz space generalizing L<sup>q*</sup>, 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.
Cuvinte cheie
metric measure space
Orlicz-Sobolev space
Orlicz-Sobolev space with zero boundary values
Poincare inequality
continuous embedding