THE RESARCH OF PERATORS ON FUNCTION SPACES BY THE METHOD TO HARMONIC ANALYSIS AND RELATED ANALYSIS

本研究的目的是利用调和分析及相关分析的方法研究函数空间上算子的性质。我们的研究人员在每个特殊的时间点都进行了研究。Sato研究了正数上的Hankel变换的一些算子与(0，pi)上的Jacobi正交系的算子之间的关系的推广。Okayasu研究了函数空间上的等距结构及其压缩Korovkin型线性逼近。此外，他还研究了Hilbert空间上的算子元组的最大部分，对该空间有一个指示的算子不等式成立。Mori研究了复空间C^m到复射影空间P^n(C)的代数非退化亚纯映射f的构造问题，证明了对于P^n(C)中任意给定的超曲面D，f都有D的亏值，Mizuhra证明了由于Morrey函数、块和Riesz势，H^1-函数的弱分解定理.应用这一结果，我们还观察到Riesz势与局部可积函数之间的交换子在Morrey空间上有界的必要性。Nakada研究了Riemann球面上有理函数Julia集的一些几何性质。特别地，它涉及到保持Julia集不变的欧几里得运动群。Kawamura讨论了关于度量空间上与混沌映射有关的概率密度函数行为的理论的推广。他考虑的空间是AL和AM空间，他推广了概率密度函数的收敛理论。利用M-obius变换的Clifford矩阵表示，Sekigawa研究了作用在三维欧几里得空间上的扭转变换的一些例子。

Our purpose of this research is to study the properties of operators on function spaces by the method of harmonic analysis and related analysis. Our investigators did the research at each special point. The content is as follows:Sato studied the generalization of the relation between some operators of Hankel transforms on the positive numbers and the operators of Jacobi orthogonal system on (0,\pi). Okayasu investigated the structure of isometries on a function space and the Korovkin type linear approximation of them by contractions. Besides, he investigated the maximum part of a tuple of operators on a Hilbert space for which an indicated operator inequality holds. Mori researched about a problem of constructions of algebraically nondegenerate meromorphic mappings f of complex spaces C^m into complex projective spaces P^n(C) that for any given hypersurface D in P^n(C), f has the prescribed deficient value for D. Mizuhra showed the weak factorization theorem of H^1-functions due to Morrey functions, blocks and the Riesz potential. Also applying this result, we observed the necessity for which the commutator between the Riesz potential and a locally integrable function to be bounded on Morrey Spaces. Nakada studied some geometric properties of the Julia set of rational functions on the Riemann sphere. In particular, it is concerned with the group of euclidean motions which keep invariant the Julia set. Kawamura discussed an generalization of the theory concerning the behavior of probability density functions associated with chaotic maps on a measure space. The spaces he considered were AL and AM spaces and he generalized a convergence theory of probability density functions. Sekigawa examined some examples of transformations with torsion acting on the 3-dimensional Euclidean space by using Clifford matrix representations of M\" obius transformation.