Newtonian spaces: An extension of Sobolev spaces to metric measure spaces | Zendy

Nageswari Shanmugalingam | Zendy

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Newtonian spaces: An extension of Sobolev spaces to metric measure spaces

Author(s) -

Nageswari Shanmugalingam

Publication year - 2000

Publication title -

revista matemática iberoamericana

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.569

H-Index - 52

eISSN - 2235-0616

pISSN - 0213-2230

DOI - 10.4171/rmi/275

Subject(s) - extension (predicate logic) , interpolation space , sobolev space , mathematics , metric space , measure (data warehouse) , birnbaum–orlicz space , pure mathematics , metric (unit) , computer science , functional analysis , business , biochemistry , chemistry , database , gene , programming language , marketing

This paper 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 paper also explores the relationship between this definition and the Hajlasz spaces. For specialized metric spaces the Sobolev embedding theorems are proven. Different versions of capacities are also explored, and these various definitions are compared. The main tool used in this paper is the concepto of moduli of path families.

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