Article
Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden
Author/s | Lerner, Andrei K.
Ombrosi, Sheldy J. Pérez Moreno, Carlos |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 2009-06 |
Deposit Date | 2016-06-15 |
Published in |
|
Abstract | 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” ... 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: sup λ>0 λw x ∈ R n : |T f(x)| Mw > λ ≤ c Z Rn |f| dx. We prove a weaker version of this inequality with M3w instead of Mw. Also we study a related question about the behavior of the constant in terms of the A1 characteristic of w. |
Funding agencies | Ministerio de Educación y Ciencia (MEC). España |
Project ID. | MTM2006-05622 |
Citation | Lerner, A.K., Ombrosi, S.J. y Pérez Moreno, C. (2009). Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden. Journal of Fourier Analysis and Applications, 15 (3), 394-403. |
Files | Size | Format | View | Description |
---|---|---|---|---|
Weak type estimates for singular ... | 194.6Kb | [PDF] | View/ | |