Título inglés | On fractional differentiation and integration on spaces of homogeneous type. |
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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 |
Acceso al artículo completo |