Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden
A well-known open problem of Muckenhoupt-Wheeden says that any Calderón-Zygmund singular integral operator T is of weak type (1,1) with respect to a couple of weights (w,Mw). In this paper, we consider a somewhat "dual" problem: supλ > 0 λ w {x ∈ ℝn: |Tf(x)|/Mw > λ} ≤ c ∫ℝn |f|,dx. W...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2009 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/79545 |
| Acceso en línea: | http://hdl.handle.net/11336/79545 |
| Access Level: | acceso abierto |
| Palabra clave: | Calderon Zygmund Operators Weights https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | A well-known open problem of Muckenhoupt-Wheeden says that any Calderón-Zygmund singular integral operator T is of weak type (1,1) with respect to a couple of weights (w,Mw). In this paper, we consider a somewhat "dual" problem: supλ > 0 λ w {x ∈ ℝn: |Tf(x)|/Mw > λ} ≤ c ∫ℝn |f|,dx. We prove a weaker version of this inequality with M 3 w instead of Mw. Also we study a related question about the behavior of the constant in terms of the A 1 characteristic of w. |
|---|