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The endpoint Fefferman-Stein inequality for the strong maximal function

 

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Opened Access The endpoint Fefferman-Stein inequality for the strong maximal function
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Author: Luque Martínez, Teresa
Parissis, Ioannis
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2014-01-01
Published in: Journal of Functional Analysis, 266 (1), 199-212.
Document type: Article
Abstract: Let Mnf denote the strong maximal function of f on Rn, that is the maximal average of f with respect to n-dimensional rectangles with sides parallel to the coordinate axes. For any dimension n > 2 we prove the natural endpoint Fefferman-Stein inequality for Mn and any strong Muckenhoupt weight w: w({x ∈ Rn : Mnf(x) > λ}) .w,n Z Rn |f(x)| λ 1 + log+ |f(x)| λ n−1 Mnw(x)dx. This extends the corresponding two-dimensional result of T. Mitsis.
Cite: Luque Martínez, T.E. y Parissis, I. (2014). The endpoint Fefferman-Stein inequality for the strong maximal function. Journal of Functional Analysis, 266 (1), 199-212.
Size: 188.8Kb
Format: PDF

URI: http://hdl.handle.net/11441/49314

DOI: 10.1016/j.jfa.2013.09.028

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