Lp bounds for Riesz transforms and square roots associated to second order elliptic operators
We consider the Riesz transforms ∇L-1/2, where L≡- divA(x)∇, and A is an accretive, n × n matrix with bounded measurable complex entries, defined on Rn. We establish boundedness of these operators on Lp(Rn), for the range pn < p ≤ 2, where pn = 2n/(n + 2), n ≥ 2, and we obtain a weak-type estimat...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2003 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:2021 |
| Acceso en línea: | https://ddd.uab.cat/record/2021 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_47203_12 |
| Access Level: | acceso abierto |
| Palabra clave: | Riesz transforms Square roots of divergence form elliptic operators |
| Sumario: | We consider the Riesz transforms ∇L-1/2, where L≡- divA(x)∇, and A is an accretive, n × n matrix with bounded measurable complex entries, defined on Rn. We establish boundedness of these operators on Lp(Rn), for the range pn < p ≤ 2, where pn = 2n/(n + 2), n ≥ 2, and we obtain a weak-type estimate at the endpoint pn. The case p = 2 was already known: it is equivalent to the solution of the square root problem of T. Kato. |
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