Potential operators associated with Jacobi and Fourier-Bessel expansions
We study potential operators (Riesz and Bessel potentials) associated with classical Jacobi and Fourier-Bessel expansions. We prove sharp estimates for the corresponding potential kernels. Then we characterize those 1≤. p, q≤. ∞, for which the potential operators are of strong type (p, q), of weak t...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universidad de La Rioja (UR) |
| Repositorio: | RIUR. Repositorio Institucional de la Universidad de La Rioja |
| OAI Identifier: | oai:portal.dialnet.es:doc/5bbc697fb750603269e81c4b |
| Acceso en línea: | https://investigacion.unirioja.es/documentos/5bbc697fb750603269e81c4b |
| Access Level: | acceso abierto |
| Palabra clave: | Fourier-Bessel expansion Fractional integral Jacobi expansion Poisson kernel Potential kernel Potential operator |
| Sumario: | We study potential operators (Riesz and Bessel potentials) associated with classical Jacobi and Fourier-Bessel expansions. We prove sharp estimates for the corresponding potential kernels. Then we characterize those 1≤. p, q≤. ∞, for which the potential operators are of strong type (p, q), of weak type (p, q) and of restricted weak type (p, q). These results may be thought of as analogues of the celebrated Hardy-Littlewood-Sobolev fractional integration theorem in the Jacobi and Fourier-Bessel settings. As an ingredient of our line of reasoning, we also obtain sharp estimates of the Poisson kernel related to Fourier-Bessel expansions. |
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