Mathematical Sciences: Imbedding and Multiplier Theorems forTriebel-Lizorkin Spaces and Spaces of Holomorphic Functions

数学科学：Triebel-Lizorkin 空间和全纯函数空间的嵌入和乘子定理

• 批准号: 9401493
• 负责人: Igor Verbitsky
• 金额: $ 2万
• 依托单位: Wayne State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-05-01 至 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401493&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Imbedding; Multiplier; Theorems

Verbitsky 9401493 This award supports mathematical research on problems related to function spaces defined on domains in several real or complex variables. The spaces, developed over the past decade play a major role in the analysis of Calderon-Zygmund and partial differential operators, are known as Triebel-Lizorkin spaces. They are refinements of the classical Sobolev and Besov spaces, developed because of the crucial role they play in wavelet-type decompositions of distributions. The basis for this work is a set of connections between weighted norm inequalities, Carleson measures, Besov spaces with zero smoothness and Hardy-Sobolev spaces in the unit of ball in complex n-dimensional space. It goals are to determine forward and reverse embedding of discrete Triebel-Lizorkin spaces into weighted sequence spaces with p-th poser norms. In addition, work will be done characterizing positive measures on the line for which the discrete maximal operator and Hilbert transform preserve the above spaces. Finally, work will continue on questions related to peak interpolation sets for the ball algebra in terms of the capacity of its subsets. Studies of the classical function spaces expanded from concerns about their structure to the application to the understanding of basic operators of more applicable analysis. As the past two decades progressed, the spaces gained their impetus from differential equations, singular operators and wavelets rather than from functional analysis. This has led to a new and vigorous blend of mathematical analysis exemplified by this proposal. ***

Verbitsky 9401493 该奖项支持与定义在多个真实的或复变量域上的函数空间相关的问题的数学研究。 在过去十年中发展起来的空间在Calderon-Zygmund和偏微分算子的分析中发挥了重要作用，被称为Triebel-Lizorkin空间。 它们是经典Sobolev和Besov空间的改进， 因为它们在分布的小波类型分解中起着至关重要的作用。 这项工作的基础是一组之间的连接加权范数不等式，Carleson措施，Besov空间与零光滑性和Hardy-Sobolev空间在单位球在复杂的n维空间。 其目标是确定离散Triebel-Lizorkin空间到具有p阶范数的加权序列空间的正嵌入和逆嵌入。 此外，工作将做的特点积极措施的线上的离散极大算子和希尔伯特变换保持上述空间。 最后，工作将继续有关的问题，峰值插值集球代数的能力，其子集。 对经典函数空间的研究从关注其结构扩展到对应用的理解，对基本算子进行了更适用的分析。 随着过去二十年的发展，空间的动力来自微分方程、奇异算子和小波，而不是泛函分析。 这导致了一个新的和充满活力的混合数学分析的例子，这一建议。 ***