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

本文的目的是研究与正交系有关的函数空间中算子的调和分析。我们的研究人员在每个特定的点进行了研究。Sato研究了Jacobi正交系统到Hankel变换系统的算子的迁移定理的推广，以及Lorentz-Zygmund空间上的算子。森推广了Nevanlinna的四值定理的情况下对集的条件的多重性。他还给定理的唯一范围集的条件，在一个角域，而不是整个复杂的平面。最后，给出了亚纯函数及其导数的一个奇异方向的存在性定理。Mizuhara研究了广义Morrey空间上的奇异积分算子及其分解算子，以及与加权哈代算子相关的权函数。此外，他还研究了Kinnunen最近关于这一点的结果， ...更多信息 Sobolev函数的Hardy-Littlewood极大函数伊势估计川村从概率论的角度研究了一维混沌映射的性质。特别是分析了Perron-Frobenius算子在Hilbert空间上移动概率密度函数的轨道，并将其与混沌映射规范地联系起来。考虑了Hankel变换的移植算子。Kanjin等人证明了移植算子将一个可积函数在一定条件下映射为一个可积函数。作为应用，他获得了L1有界和H1有界的塞萨罗运营商的汉克尔变换。Kanjin在可积函数空间的Hermite和Laguerre展开中建立了Hardy型不等式。Miyachi在欧氏整环上引入了加权哈代空间，并建立了这些空间的几个基本性质。利用他的加权哈代空间，他扩展了经典的雅可比级数的移植定理的情况下，指数p小于或等于1。他还证明，修改希尔伯特变换定义通过ultraspherical系列是有界的加权哈代空间，并应用这一结果，他广义的伯克霍尔德-甘迪-西尔弗斯坦定理有关的真实的变量表征的哈代类的情况下，他的加权哈代类的开放区间。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