Article
The endpoint Fefferman-Stein inequality for the strong maximal function
Author/s | Luque Martínez, Teresa
Parissis, Ioannis |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 2014-01-01 |
Deposit Date | 2016-11-29 |
Published in |
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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 ... 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. |
Funding agencies | Ministerio de Economía y Competitividad (MINECO). España Academy of Finland |
Project ID. | info:eu-repo/grantAgreement/MINECO/BES-2010-030264
138738 |
Citation | 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. |
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