On fractional differentiation and integration on spaces of homogeneous type.

Título inglés On fractional differentiation and integration on spaces of homogeneous type.
Título español Diferenciación e integración fraccionales sobre espacios de tipo homogéneo.
Autor/es Gatto, A. Eduardo ; Segovia, Carlos ; Vági, Stephen
Organización DePaul Univ., Chicago (Illinois), Estados Unidos;Univ. Buenos Aires - CONICET, Buenos Aires, Argentina
Revista 0213-2230
Publicación 1996, 12 (1): 111-145, 15 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés In this paper we define derivatives of fractional order on spaces of homogeneous type by generalizing a classical formula for the fractional powers of the Laplacean [S1], [S2], [SZ] and introducing suitable quasidistances related to an approximation of the identity. We define integration of fractional order as in [GV] but using quasidistances related to the approximation of the identity mentioned before.
We show that these operators act on Lipschitz spaces as in the classical cases. We prove that the composition Tα of a fractional integral Iα and a fractional derivative Dα of the same order and its transpose (a fractional derivative composed with a fractional integral of the same order) are Calderón-Zygmund operators. We also prove that for small order α, Tα is an invertible operator in L2. In order to prove that Tα is invertible we obtain Nahmod type representations for Iα and Dα and then we follow the method of her thesis [N1], [N2].
Clasificación UNESCO 120201
Palabras clave español Operadores diferenciales ; Operadores integrales ; Espacio de Lipschitz ; Espacio homogéneo ; Kernel
Código MathReviews MR1387588
Código Z-Math Zbl 0921.43005
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