HARMONIC ANALYSIS IN THE OPERATORS OF THE FUNCTION SPACES RELATED TO THE ORTHOGONAL SYSTEMS

本研究的目的是研究正交系统相关函数空间算子的调和分析。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研究了从Jacobi正交系统到Hankel变换系统的算子以及Lorentz-Zygmund空间上算子的迁移定理的推广。Mori将Nevanlinna的四值定理推广到具有多重条件的对集的情况。他还给出了在角域而不是整个复平面条件下的唯一值域集的定理。最后给出了一类亚纯函数及其导数的共享值问题的奇异方向的存在性定理。Mizuhara研究了广义Morrey空间上的一些奇异积分算子及其对易子，以及与加权Hardy算子相关的一些权函数。此外，他还研究了最近Kinnunen关于Sobolev函数的Hardy-Littlewood极大函数的估计的结果。Kawamura从概率论的角度研究了一维混沌映射的性质。他特别分析了由Perron-Frobenius算子移动的概率密度函数在Hilbert空间上的轨道，这是混沌映射的典型概念。考虑了汉高变换的移植算子。Kanjin证明了移植算子在一定条件下将一个可积函数映射为一个可积函数。作为应用，他得到了Hankel变换的Cesaro算子的l1有界性和h1有界性。Kanjin在可积函数空间的Hermite和Laguerre展开中建立了hardy型不等式。Miyachi在欧几里得域上引入了加权Hardy空间，并建立了这些空间的几个基本性质。利用他的加权Hardy空间，他将Jacobi级数的经典移植定理推广到指数p小于等于1的情况。他还证明了由超球级数定义的修正Hilbert变换在他的加权Hardy空间中是有界的，并应用这一结果，将关于Hardy类的实变量表征的Burkholder-Gundy-Silverstein定理推广到他的加权Hardy类在开区间上的情况。少

Our purpose of this research is to study Harmonic Analysis in the operators of the function spaces related to the orthogonal systems. Our investigators did the research at each special point. The content is as followsSato studied the generalization of a transference theorem related to the operators from Jacobi orthogonal systems to Hankel transform systems, and the operators on Lorentz-Zygmund spaces. Mori generalized the Nevanlinna's four values theorem to the case of pair sets with conditions of multiplicities. He also gave theorems for unique range sets with conditions in an angular domain instead of the whole complex plane. Finally, he gave existence theorems of a singular direction for a shrare value problem of a meromorphic function and its derivative. Mizuhara studied some singular integal operators and its commutators on generalized Morrey spaces and some weight functions related to the weighted Hardy operators. Also, he studied recent Kinnunen's results concerning to the poinw … More ise estimates of the Hardy-Littlewood maximal function of a Sobolev function. Kawamura studied the property of one-dimensional chaotic maps in the view of probability theory. Especially he analyzed the orbit of a probability density function moved by the Perron-Frobenius operator on Hilbert space, which is canonically associated with chaotic map. The transplantation operators for the Hankel transform were considered. Kanjin have proved that the transplantation operator maps an integrable function under certain conditions to an integrable function. As an application, he obtained the L1-boundedness and H1-boundedness of Cesaro operators for the Hankel transform. Kanjin established Hardy-type inequalities in the Hermite and Laguerre expansions for the space of integrable functions. Miyachi introduced weighted Hardy spaces on a Euclidean domain and established several fundamental properties of these spaces. Using his weighted Hardy spaces, he extended classical transplantation theorem for Jacobi series to the case of the exponent p less than or equal to 1. He also proved that the modified Hilbert transform defined through ultraspherical series is bounded in his weighted Hardy spaces, and applying this result, he generalized the Burkholder-Gundy-Silverstein theorem concerning the real variable characterization of Hardy classes to the case of his weighted Hardy classes on the open interval. Less