Maximal estimates for a generalized spherical mean Radon transform acting on radial functions
We study a generalized spherical means operator, viz.\ generalized spherical mean Radon transform, acting on radial functions. As the main results, we find conditions for the associated maximal operator and its local variant to be bounded on power weighted Lebesgue spaces. This translates, in partic...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Basque Center for Applied Mathematics (BCAM) |
| Repositorio: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/1073 |
| Acceso en línea: | http://hdl.handle.net/20.500.11824/1073 |
| Access Level: | acceso embargado |
| Palabra clave: | Spherical Radon transform spherical mean maximal operator radial function weighted estimate wave equation Euler-Poisson-Darboux equation axially symmetric solution convergence to initial data |
| Sumario: | We study a generalized spherical means operator, viz.\ generalized spherical mean Radon transform, acting on radial functions. As the main results, we find conditions for the associated maximal operator and its local variant to be bounded on power weighted Lebesgue spaces. This translates, in particular, into almost everywhere convergence to radial initial data results for solutions to certain Cauchy problems for classical Euler-Poisson-Darboux and wave equations. Moreover, our results shed some new light on the interesting and important question of optimality of the yet known $L^p$ boundedness results for the maximal operator in the general non-radial case. It appears that these could still be notably improved, as indicated by our conjecture of the ultimate sharp result. |
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