  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.
