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Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden

 

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Opened Access Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden
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Author: Lerner, Andrei K.
Ombrosi, Sheldy J.
Pérez Moreno, Carlos
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2009-06
Published in: Journal of Fourier Analysis and Applications, 15 (3), 394-403.
Document type: Article
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” 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.
Cite: 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.
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URI: http://hdl.handle.net/11441/42363

DOI: 10.1007/s00041-008-9032-2

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