A generalization of Orlicz-Sobolev spaces on metric measure spaces via Banach function spaces

We show that several basic definitions and results regarding modulus, capacity and Orlicz-Sobolev spaces on metric measure spaces can be generalized to the case where the role of the Orlicz space is played by an abstract Banach function space B. This new general setting could bring a new perspective in the study of Sobolev-type spaces on metric measure spaces, due to the great generality of Banach function spaces. We prove several properties of the newly introduced Sobolev-type space N-1,N-B (X), including its completeness and a Mazur-type theorem.