在本篇文章中，我們利用由林欽誠教授及李明憶所發展的加權哈弟空間
(weighted Hardy space)上的分子特徵來証明郝曼德乘算子
(Hormander''s multipliers)在加權赫茲形式哈弟空間 (weighted
Herz-type Hardy spaces) $Hdot K_2^{alpha,p}(|x|^t;|x|^t)$
and $HK_2^{alpha,p}(|x|^t;|x|^t)$上的有界性。

In this article, we apply the molecular characterization of the weighted
Hardy space developed by the first two authors to show the boundedness of
Hormander multiplier on the weighted Herz-type Hardy spaces
$Hdot K_2^{alpha,p}(|x|^t;|x|^t)$ and $HK_2^{alpha,p}(|x|^t;|x|^t)$.

[BS] A. Baernstein II and E. T. Sawyer, Embedding and multiplier theorems
for Hp(Rn), Mem. Amer. Math. Soc. 53 (1985).
[Be] A. Beurling, Construction and analysis of some convolution algebras,
Ann. Inst. Fourier Grenoble 14 (1964), 1-32.
[CF] R. Coifman and C. Fe erman, Weighted norm inequalities for maximal
functions and singular integrals, Studia Math. 51 (1974), 241-250.
[Fe] H. G. Feichtinger, An elementary approach to Wiener’s third
Tauberian theorem for the Euclidean n-spaces, Proceedings of Conference
at Cortona 1984, Symposia Mathematica 29, Academic Press, New
York (1987), 267-301.
[Fl] T. M. Flett, Some elementary inequalities for integrals with applications
to Fourier transforms, Proc. London Math. Soc. (3) 29 (1974), 538-556.
[GR] J. Garcia-Cuerva and J. Rubio de Francia, Weighted Norm Inequalities
and Related Topics, North Holland, 1985.
[He] C. Herz, Lipschitz spaces and Bernstein’s theorem on absolutely convergent
Fourier transforms, J. Math. Mech. 18 (1968), 283-324.
[HMW] R. Hunt, B. Muckenhoupt, and R. Wheeden, Weighted norm inequalities
for the conjugate function and Hilbert transform, Trans. Amer. Math.
Soc. 176 (1973), 227-251.
[LL] Ming-Yi Lee and Chin-Cheng Lin, The molecular characterization of
weighted Hardy spaces, J. Funct. Anal. 188 (2002), 442-460.
[LY1] S. Lu and D. Yang, The decomposition of the weighted Herz spaces and
its applications, Sci. in China (Ser. A) 38 (1995), 147-158.
[LY2] , The weighted Herz-type Hardy spaces and its applications, Sci.
in China (Ser. A) 38 (1995), 662-673.
[LY3] , The local versions of Hp(Rn) spaces at the origin, Studia Math.
116 (1995), 103-131.
[M] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal
function, Trans. Amer. Math. Soc. 165 (1972), 207-226.
[ST] J.-O. Str¨omberg and A. Torchinsky, Weighted Hardy Spaces, Lecture
Notes in Mathematics, vol. 1381, Springer-Verlag, 1989.
[TW] M. H. Taibleson and G.Weiss, The molecular characterization of certain
Hardy spaces, Ast´erisque 77 (1980), Soci´et´e Math. de France, Paris, 67-
149.