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小波与Hardy空间和BMO空间上的乘子

发表时间:2011-07-15  浏览量:1386  下载量:618
全部作者: 杨奇祥
作者单位: 武汉大学数学与统计学院
摘 要: 20世纪50年代以来,主要采用Sobolev空间在紧集上的容量刻画乘子空间并由此出发研究乘子的应用,部分乘子空间没有无条件基。考虑端点空间的情形,端点空间有其特殊性,引进小波,通过原子分解、函数乘积的特殊分解、函数空间的小波刻画、对偶等关系分析分数次Hardy空间和分数次BMO空间上乘子空间的结构。得出前者乘子空间只有0元素,后者乘子空间的元素是2个特殊空间的交。
关 键 词: 基础数学;实分析;乘子空间;Daubechies基;函数乘积的分解;分数次Hardy空间;分数次BMO空间
Title: Wavelet characterization for multipliers on Hardy space and BMO space
Author: YANG Qixiang
Organization: School of Mathematics and Statistics, Wuhan University
Abstract: In this paper, wavelet characterization of multiplier spaces for the end point space cases has been considered. Multiplier spaces have been studied heavily since 1950s and stay always as an active topic. Before, one used the capacity of compact set on Sobolev spaces to characterize multiplier spaces and to study the applications related to multiplier spaces. Part of multiplier spaces has no unconditional basis. Here wavelet methods and atomic decomposition are introduced, and the structure of multiplier spaces is analyzed through the following conceptions: some special decomposition of function product, known wavelet characterization of certain function spaces, dual property etc. The multiplier spaces on fractional Hardy spaces has only element 0 and the multiplier spaces on fractional BMO is the intersection of two special spaces.
Key words: fundamental mathematics real analysis; multiplier spaces; Daubechies wavelet; decomposition of function product; fractional Hardy space; fractional BMO spaces
发表期数: 2011年7月第13期
引用格式: 杨奇祥. 小波与Hardy空间和BMO空间上的乘子[J]. 中国科技论文在线精品论文,2011,4(13):1149-1154.
 
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