Mixed weak estimates of Sawyer type for commutators of generalized singular integrals and related operators
We study mixed weak type inequalities for the commutator [b,T], where b is a BMO function and T is a Calderón-Zygmund operator. Our technique involves the classical Calderón–Zygmund decomposition, which allows us to give a direct proof without taking into account the associated maximal operator. We...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/167892 |
| Acceso en línea: | http://hdl.handle.net/11336/167892 |
| Access Level: | acceso abierto |
| Palabra clave: | MUCKENHOUPT WEIGHTS BMO COMMUTATORS https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | We study mixed weak type inequalities for the commutator [b,T], where b is a BMO function and T is a Calderón-Zygmund operator. Our technique involves the classical Calderón–Zygmund decomposition, which allows us to give a direct proof without taking into account the associated maximal operator. We use this result to prove an analogous inequality for higher-order commutators. For a given Young function φ we also consider singular integral operators T whose kernels satisfy a Lφ-Hörmander property, and we find sufficient conditions on φ such that a mixed weak estimate holds for T and also for its higher order commutators T m b . We also obtain a mixed estimation for a wide class of maximal operators associated to certain Young functions of LlogL type which are in intimate relation with the commutators. This last estimate involves an arbitrary weight u and a radial function v which is not even locally integrable. |
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