A generalization of the boundedness of certain integral operators in variable lebesgue spaces
Let n ε N. Let A1, ...Am be n×n invertible matrices. Let 0 ≤ α < n and 0 < αi < n such that α1 +...+αm = n-α . We define In [8] we obtained the boundedness of this operator from Lp(.)(Rn) into Lq(.)(Rn) for 1/q(.) = 1/p(.) - α/n, in the case that Ai is a power of certain fixed matrix A and...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2020 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/143432 |
| Acceso en línea: | http://hdl.handle.net/11336/143432 |
| Access Level: | acceso abierto |
| Palabra clave: | FRACTIONAL INTEGRALS VARIABLE EXPONENTS https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | Let n ε N. Let A1, ...Am be n×n invertible matrices. Let 0 ≤ α < n and 0 < αi < n such that α1 +...+αm = n-α . We define In [8] we obtained the boundedness of this operator from Lp(.)(Rn) into Lq(.)(Rn) for 1/q(.) = 1/p(.) - α/n, in the case that Ai is a power of certain fixed matrix A and for exponent functions p satisfying log-Hölder conditions and p(Ay) = p(y), y ε Rn. We will show now that the hypothesis on p, in certain cases, is necessary for the boundedness of Tα and we also prove the result for more general matrices Ai. |
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