Abstract
We generalize a coincidence result from the case of Sobolev-type spaces to the case of Orlicz-Sobolev spaces corresponding to a doubling Young function, in the setting of doubling metric measure spaces. We consider three types of Orlicz-Sobolev spaces: (i) a space of Newtonian type; (ii) a space associated to a generalized Poincaré inequality; (iii) a space defined as the closure of the class of Orlicz functions that are locally Lipschitz, under some norm involving an abstract differential operator.
Cuvinte cheie
metric measure space
weak upper gradient
Orlicz-Sobolev space
locally Lipschitz func-tions
Orlicz-Poincaré inequality