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arXiv · 1211.2950

The endpoint Fefferman-Stein inequality for the strong maximal function

Teresa Luque·Ioannis Parissis
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Abstract

Let Mf denote the strong maximal function of f on R^n, that is the maximal average of f with respect to n-dimensional rectangles with sides parallel to the coordinate axes. For any dimension n>1 we prove the natural endpoint Fefferman-Stein inequality for M and any strong Muckenhoupt weight w: w({x \in R^n: M f (x) > t}) \lesssim_{w,n} \int_{R^n} |f|/t [1 + (log^+ |f|/t)^{n-1}] Mw. This extends the corresponding two-dimensional result of T. Mitsis.

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BibTeXRIS

Teresa Luque, Ioannis Parissis. 2012-11-13. The endpoint Fefferman-Stein inequality for the strong maximal function. https://doi.org/10.1016/j.jfa.2013.09.028

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