Boundedness and unboundedness results for some maximal operators on functions of bounded variation
We characterize the space BV (I) of functions of bounded variation on an arbitrary interval I ⊂ R, in terms of a uniform boundedness condition satisfied by the local uncentered maximal operator MR from BV (I) into the Sobolev space W1, 1 (I). By restriction, the corresponding characterization holds...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2008 |
| País: | España |
| Recursos: | Universidad de La Rioja (UR) |
| Repositorio: | RIUR. Repositorio Institucional de la Universidad de La Rioja |
| OAI Identifier: | oai:portal.dialnet.es:doc/5bbc687fb750603269e80a0b |
| Acesso em linha: | https://investigacion.unirioja.es/documentos/5bbc687fb750603269e80a0b |
| Access Level: | acceso abierto |
| Palavra-chave: | Bounded variation functions Maximal function Sobolev spaces |
| Resumo: | We characterize the space BV (I) of functions of bounded variation on an arbitrary interval I ⊂ R, in terms of a uniform boundedness condition satisfied by the local uncentered maximal operator MR from BV (I) into the Sobolev space W1, 1 (I). By restriction, the corresponding characterization holds for W1, 1 (I). We also show that if U is open in Rd, d > 1, then boundedness from BV (U) into W1, 1 (U) fails for the local directional maximal operator MTv, the local strong maximal operator MTS, and the iterated local directional maximal operator MTd ○ ⋯ ○ MT1. Nevertheless, if U satisfies a cone condition, then MTS : BV (U) → L1 (U) boundedly, and the same happens with MTv, MTd ○ ⋯ ○ MT1, and MR. © 2007 Elsevier Inc. All rights reserved. |
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