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

Autores: Nageswari Shanmugalingam
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 16, Nº 2, 2000, págs. 243-280
Idioma: inglés
DOI: 10.4171/rmi/275
Títulos paralelos:
- Espacios newtonianos: una extensión de los espacios de Sobolev a los espacios métricos de medida.
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Resumen
- 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.