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研究生:林有鈿
研究生(外文):Yu-Tien Lin
論文名稱:加權赫茲形式哈弟空間上的郝曼德乘算子
論文名稱(外文):Hormander's multipliers for the weighted Herz-type Hardy spaces
指導教授:林欽誠
指導教授(外文):(Chin-Cheng Lin
學位類別:碩士
校院名稱:國立中央大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:19
中文關鍵詞:加權赫茲形式哈弟空間郝曼德乘算子
外文關鍵詞:weighted Herz-type Hardy spacesHormander's multipliers
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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 $HK_2^{alpha,p}(|x|^t;|x|^t)$.


1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2. The Ap weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3. The atomic decomposition and molecular characterization . . 7
4. Main results and applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
5. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19


[BS] A. Baernstein II and E. T. Sawyer, Embedding and multiplier theoremsfor 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 maximalfunctions and singular integrals, Studia Math. 51 (1974), 241-250.[Fe] H. G. Feichtinger, An elementary approach to Wiener’s thirdTauberian theorem for the Euclidean n-spaces, Proceedings of Conferenceat Cortona 1984, Symposia Mathematica 29, Academic Press, NewYork (1987), 267-301.[Fl] T. M. Flett, Some elementary inequalities for integrals with applicationsto Fourier transforms, Proc. London Math. Soc. (3) 29 (1974), 538-556.[GR] J. Garcia-Cuerva and J. Rubio de Francia, Weighted Norm Inequalitiesand Related Topics, North Holland, 1985.[He] C. Herz, Lipschitz spaces and Bernstein’s theorem on absolutely convergentFourier transforms, J. Math. Mech. 18 (1968), 283-324.[HMW] R. Hunt, B. Muckenhoupt, and R. Wheeden, Weighted norm inequalitiesfor 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 ofweighted Hardy spaces, J. Funct. Anal. 188 (2002), 442-460.[LY1] S. Lu and D. Yang, The decomposition of the weighted Herz spaces andits 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 maximalfunction, Trans. Amer. Math. Soc. 165 (1972), 207-226.[ST] J.-O. Str¨omberg and A. Torchinsky, Weighted Hardy Spaces, LectureNotes in Mathematics, vol. 1381, Springer-Verlag, 1989.[TW] M. H. Taibleson and G.Weiss, The molecular characterization of certainHardy spaces, Ast´erisque 77 (1980), Soci´et´e Math. de France, Paris, 67-149.

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