The Riesz potential as a multilinear operator into general BMOβ spaces

Given α > 0 and a space of homogeneous type X, n-normal, with n ℝ+, we consider an extension of the standard multilinear fractional integral on Lp1 × ... × Lpk for the range of 1/pi = 1/p1...+1/pk -α/n ≤ 0. We show that the target space is an adequate space BMOβ defined through mean oscillations....

Descripción completa

Detalles Bibliográficos
Autores: Aimar, Hugo Alejandro, Hartzstein, Silvia Inés, Iaffei, Bibiana Raquel, Viviani, Beatriz Eleonora
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2011
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/84086
Acceso en línea:http://hdl.handle.net/11336/84086
Access Level:acceso abierto
Palabra clave:Riesz Potentials
Multilinear Operators
Lipschitz Integral Spaces
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:Given α > 0 and a space of homogeneous type X, n-normal, with n ℝ+, we consider an extension of the standard multilinear fractional integral on Lp1 × ... × Lpk for the range of 1/pi = 1/p1...+1/pk -α/n ≤ 0. We show that the target space is an adequate space BMOβ defined through mean oscillations. For general spaces of homogeneous type this is a Banach space of classes of functions modulii constants and the range of β is [0, 1). However, if X = ℝn (n ∈ N), we can extend the result to β > 0 taking in account that BMOβ is a space of classes modulii polynomials of order lower than or equal to [β]. Bibliography: 15 titles.