摘要
Let K<sub>δ</sub>, 0【δ1, be the Kakeya maximal operator defined as the supremum of averagesover tubes of the eccentricity δ. The （so-called） Fefferman-Stein-type inequality: ‖K<sub>δ</sub>f‖<sub>L<sup>d</sup></sub>（R<sup>d</sup>,w）≤C<sub>d</sub>（1/δ）<sup>（d-2）/2d</sup>（log（1/δ））<sup>α<sub>d</sub></sup>‖f‖<sub>L<sup>d</sup>（R<sup>d</sup>,K<sub>δ</sub>w）</sub> is shown, where C<sub>d</sub> and α<sub>d</sub> are constants depending only onthe dimension d and w is a weight. The result contains the exponent （d-2）/2d which is smaller thanthe exponent （d-2）（d-1）/d（2d-3） obtained in [7].
Let K<delta>, 0 < <delta>±1, be the Kakeya maximal operator defined as the supremum of averages over tubes of the eccentricity <delta>. The (so-called) Fefferman-Stein-type inequality: $|| {K_\delta f} ||_{L^d({{\rm R}^d,w})} \le C_d ({1 \over \delta})^{(d - 2)/2d}(\log ({1 \over \delta } ))^{\alpha_d} || f ||_{L^d ({\rm R}^d,K_{\delta}w})}$is shown, where Cd and <alpha>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].
基金
Supported by Japan Society for the Promotion of Sciences and Fujukai Foundation.
