Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
The author studies a possible definition of Sobolev spaces in abstract metric spaces, and answers in the affirmative the question whether this definition yields a Banach space. The author also explores the relationship between this definition and the Sobolev spaces defined by Hajłasz. For specialized metric spaces, the Sobolev embedding theorems are established. Different versions of capacities are also explored, and these various definitions are compared. The main tool used in this paper is the concept of moduli of path families.
scientific article; zbMATH DE number 1563249