R~3上一类圆盘型Besicovitch集的Hausdorff维数估计
|
摘要
文中研究了R~3上一类圆盘型Besicovitch集的Hausdorff维数,将Kakeya问题二维情形的其中一种证明方法推广到R~3空间,证明了该类圆盘型Besicovitch集的Hausdorff维数为3.
This dissertation is devoted to the Hausdorff dimension for a type of disc Besicovitch sets. It is well known that the situation of R~2 about Kakeya problem has been solved. There exist several methods which can prove it. One of those methods to R~3 space is generalized in this paper. It is proved that there are a type of disc Besicovitch sets in R~3 whose Hausdorff dimension is R~3.
This dissertation is devoted to the Hausdorff dimension for a type of disc Besicovitch sets. It is well known that the situation of R~2 about Kakeya problem has been solved. There exist several methods which can prove it. One of those methods to R~3 space is generalized in this paper. It is proved that there are a type of disc Besicovitch sets in R~3 whose Hausdorff dimension is R~3.
引文
[1] CORDOBA A. The Kakeya maximal function and the spherical summation multipliers[J]. American Journal of Mathematics,1977,99(1):1-22.
[2] BOURGAIN J. Besicovitch type maximal operators and applications to Fourier analysis Geometric[J].Functional Analysis Gafa,1991,1(2):147-187.
[3] FALCONER K J. Fractal geometry-mathematical foundations and applications[M]. 2nd ed. England:Willey Publishing Inc,1990.
[4] CHRIST M,DUOANDIKOETXEA J,RUBIO DE FRANCIA J L. Maximal operators associated to the Radon transform and the Calderon-Zygmund method of rotations[J]. Duke Math J, 1986, 53(1):189-209.
[5] WOLFF T. An improved bound for Kakeya type maximal functions[J]. Revista Mat Iberoamericana,1995,11(3):651-674.
[6] KATZ N H,TAO T. New bounds for Kakeya problems[J]. J Anal Math,2002,87(1):231-263.
[2] BOURGAIN J. Besicovitch type maximal operators and applications to Fourier analysis Geometric[J].Functional Analysis Gafa,1991,1(2):147-187.
[3] FALCONER K J. Fractal geometry-mathematical foundations and applications[M]. 2nd ed. England:Willey Publishing Inc,1990.
[4] CHRIST M,DUOANDIKOETXEA J,RUBIO DE FRANCIA J L. Maximal operators associated to the Radon transform and the Calderon-Zygmund method of rotations[J]. Duke Math J, 1986, 53(1):189-209.
[5] WOLFF T. An improved bound for Kakeya type maximal functions[J]. Revista Mat Iberoamericana,1995,11(3):651-674.
[6] KATZ N H,TAO T. New bounds for Kakeya problems[J]. J Anal Math,2002,87(1):231-263.