THE RESEARCH OF OPERATORS ON FUNCTION SPACES RELATED TO HARMONIC ANALYSIS

调和分析相关函数空间算子的研究

基本信息

批准号：
12640151
负责人：
SATO Enji
金额：
$ 1.98万
依托单位：
YAMAGATA UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2001
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640151/
关键词：
Fourier transform Lorentz space positive trigonometric polynomial deficiency rational mapping singular integral hausdorff dimension Banach lattice 交換子極限集合カオス写像 Essentially definite operators 有理型曲線除外値複素力学系カオス力学系

项目摘要

Our purpose of this research is to study the properties of operators on function spaces related to harmonic analysis. Our investigators did the research at each special point. The content is as follows:Sato studied the properties of some bounded linear operators on Lorentz space associated with a measure space. In particular, by the application of the relation between Hankel transforms and Jacobi orthogonal system, he got the similar result with respect to the Lorentz multipliers of Jacobi orthogonal system to the result with respect to some bounded linear operators on the Lorentz space associated with Hankel transforms. Okayasu researched on essential definiteness, and semidefiniteness for tuples of operators, and Fejer's theorem on coefficients of positive trigonometric polynomials. Also he studied Korovkin type theorems on positive mappings of function spaces, essentially semidefinite operators, and positive trigonometric polynomials, and Korovkin type approximation. Mori has been d … More ealt with elimination theorems of defects of meroraorphic mappings of C"m into P"n(C). He showed an elimination theorem of defects of hypersurfaces in P"n(C) for a holomorphi curve of C into P"n(C), before. In this time, he proved an elimination theorem of defects of hypersurfaces in P"n(C) for a meroraorphic mapping of C"m into P"n(C). Mizuhara showed the weak factorization theorem of Lp-functions due to Morrey functions, blocks and the Riesz potential. Also applying this result, he showed the necessity for which the commutator between the Riesz potential and a locally integrable function to be bounded on Lp-spaces. Nakada studied the following: Let L be the limit set of a discontinuous group of Mobius transformations and let J be the Julia set of a rational function on the Riemann sphere. He studied the t-dimensional invariant probability measure on L and J to estimate the hausdorff dimension of these singular sets. Kawamura studied a generalization of chaotic maps to maps with n laps on a measure space and the behavior of the orbit of a probability density function. In this study he obtained some results concerning linear operators and Banach lattices. Sekigawa examined some exapraples of rational functions to study the connectivity of components of Fatou sets. He studied an inequality on the n-th derivatives of holomorphic functions of the open unit disk into itself. Less

这项研究的目的是研究操作员在与谐波分析有关的功能空间上的特性。我们的调查人员在每个特殊点进行了研究。内容如下：SATO研究了一些有界线性操作员在与测量空间相关的Lorentz空间上的属性。特别是，通过将Hankel变换与Jacobi正交系统之间的关系应用，他在Jacobi正交系统的Lorentz乘数上获得了相似的结果，而与与Hankel变换相关的Lorentz空间上的某些有界线性算子方面的结果。 Okeasu研究了基本定义和对操作员元素的半精力，以及Fejer的定理关于阳性三角多项主义的系数。他还研究了Korovkin型定理在功能空间的正映射，本质上是半金属运算符和阳性三角多项式和Korovkin型近似值上。莫里（Mori）一直是……消除了c“ m中的meror型映射缺陷理论，c” m in p“ n（c）。他在p“ n（c）中，c” n（c）中c的Holomorphi曲线的缺陷表现出了消除理论。在这段时间里，他证明了p“ n（c）中的超曲面缺陷的理论，用于将c“ m绘制到p” n（c）中的meror型映射中。瑞马拉（c）n（c）。瑞马拉（c）n（c）表明了由于莫雷功能，障碍和ries势的范围，他在这种情况下的界限也表现出了在这种情况下的范围。他还适用于该效果。 LP空间。在本研究中，测量空间和概率密度功能的轨道。他研究了开放单元磁盘的全体形态功能的第n个衍生物的不平等。较少的