THE RESEARCH OF OPERATORS ON FUNCTION SPACES RELATED TO HARMONIC ANALYSIS

本研究的目的是研究与调和分析相关的函数空间上算子的性质。我们的调查人员在每个特殊的地点都做了调查。内容如下：Sato研究了与测度空间相关的Lorentz空间上的一些有界线性算子的性质。特别地，通过应用Hankel变换与Jacobi正交系统之间的关系，他得到了关于Jacobi正交系统的Lorentz乘子的结果与关于与Hankel变换相关的Lorentz空间上的一些有界线性算子的结果相似。Okayasu研究了算子元组的本质确定性和半确定性，以及关于正三角多项式系数的Fejer定理。他还研究了关于函数空间正映射的Korovkin型定理，本质上是半定算子，正三角多项式，以及Korovkin型近似。Mori对C ' m到P ' n(C)的纯纯映射缺陷的消去定理做了更多的研究。对于C到P ' n(C)的全纯曲线，他给出了P ' n(C)中超曲面缺陷的消去定理。在这一次，他证明了一个C“m”到P“n(C)的纯纯映射在P”n(C)中的超曲面缺陷的消去定理。Mizuhara给出了基于Morrey函数、块和Riesz势的lp函数的弱分解定理。同样应用这个结果，他证明了Riesz势和局部可积函数之间的对易子在lp空间上有界的必要性。Nakada研究了以下问题：设L为不连续莫比乌斯变换群的极限集，设J为黎曼球上有理函数的Julia集。他研究了L和J上的t维不变概率测度来估计这些奇异集的豪斯多夫维数。Kawamura研究了混沌映射在测量空间上的推广到n圈的映射，以及概率密度函数的轨道行为。在这项研究中，他得到了关于线性算子和巴拿赫格的一些结果。Sekigawa考察了一些有理函数的例子来研究法头集各部分的连通性。他研究了开单位盘的全纯函数对其自身的n阶导数的不等式。少

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