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....
| Autores: | , , , |
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| 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 |
| 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. |
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