The Fefferman-Stein-Type Inequality for the Kakeya Maximal Operator II

Let K _δ, 0 < δ≪1, be the Kakeya maximal operator defined as the supremum of averages over tubes of the eccentricity δ. The (so-called) Fefferman-Stein-type inequality: is shown, where C _d and α _d are constants depending only on the dimension d and w is a weight. The result contains the exponent (d−2)/2d which is smaller than the exponent (d−2)(d−1)/d(2d−3) obtained in 7]. Received October 8, 2001, Accepted February 28, 2002