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

Lerner, Andrei K. et al · Birkhäuser Publishing · 2009

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Author / responsible party
Lerner, Andrei K. et al
Publisher
Birkhäuser Publishing
Year
2009
ISSN
1069-5869
ISSN
1069-5869
Language
English

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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. Fil: Lerner, Andrei K.. Universidad de Sevilla; España Fil: Ombrosi, Sheldy Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina

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APA 7

Lerner, A. K. E. A. (2009). Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden. http://hdl.handle.net/11336/79545

MLA

Lerner, Andrei K. et al. "Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden." 2009. http://hdl.handle.net/11336/79545.

Chicago

Lerner, Andrei K. et al. 2009. "Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden.". http://hdl.handle.net/11336/79545.

Harvard

Lerner, A. K. E. A. 2009, Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden, Birkhäuser Publishing, available at: http://hdl.handle.net/11336/79545 [Accessed 9 Aug. 2026].

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Title
Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden
Author / contributors
Lerner, Andrei K. et al
Publisher
Birkhäuser Publishing
Publication year
2009
ISSN
1069-5869
ISSN
1069-5869
Language
English

Subjects

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Calderon; Zygmund Operators; Weights; https://purl.org/becyt/ford/1.1; https://purl.org/becyt/ford/1
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