THE RESEARCH OF WEAK TYPE OPERATORS ON FUNCTION SPACES

函数空间弱型算子的研究

• 批准号: 09640150
• 负责人: SATO Enji
• 金额: $ 1.41万
• 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: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640150/
• 关键词: Fourier multiplier; Hermitian Banach*-algebras; value distribution theory; commutator; discontinuous; wavelet thery; Clifford matrix; self-dual codes; エルミート的Banach^*-環; ウエブレット理論; クリフォード行列; 自己双対コード; フーリエアルチプライヤー; Heingの不等式; 有理型写像; Nevanlinna

Sato studied the properties of Fourier multipliers on locally Compact abelian groups. In particular, he got some results with respect to Lp-improving multipliers and Lorentz-improving multipliers, and published the results. Okayasu studied that the Lowner-Heinz inequality was shown for strictly positive elements of unital hermitian Banacb*-algebras, via the Cordes inequality which was also shown for same objects. Also be studied that several results were gotten on linear isometries on function spaces, and on operator spaces. Mon got an elimination theorem of Nevanlinna defects of holomorphic curves into Pn(C) for rational moving targets. Also, he considered to introduce a distance in the space of holomorpbic(or meromorphic) mappings into Pn(C), and obtained a distance in this space. Then holomorphic (or mieromorphic) mappings into Pn(C) without Nevanlinna defects are densein this space. Itizuhara showed the boundedness of commutators (b, T], between some singular integral operator and … More multiplication operator by a locally integrable function bon Morrey spaces Lpg(Rn) with general growth function g, This results generalize partly the classical results due to Di Fazio and Ragusa. Also he obtained some new results. Nakada studied the following subject by the method of complex analysis. Firstly, the region of discontinuities and the limit sets of discontinuous groups acting on the Riemann sphere. Secondary, the Fatou sets and Julia sets arise from complex dynamics of rational maps of the Riemarin sphere. Kawamura studied some chaotic properties in topological dynamical systems by using the theory of operator algebras. Considering topological dynamical systems in the sense of probability theory, he tried to analyze them on the Hubert space and obtained some relations between our study of topological dynamics and wavelet theory. Sekigawa investigated the Ford fundamental regions for the cyclic groups generated by some parabolic Mobius transformations acting on the 3-dimensional Euclidean space, by using the Clifford matrix representation of liobius transformations. Harada studied algebraic theory of coding theory over finite rings, and codes over finite rings with relationships to other topics. Less

Sato研究了傅立叶乘数在局部紧凑的Abelian组上的性质。特别是，他在LP改造的乘数和Lorentz-Improving乘数方面取得了一些结果，并发布了结果。 Okeasu研究表明，下海因兹的不等式显示了单位Hermitian banacb*-ergebras的严格阳性元素，该元素通过电线不平等现象也显示了相同的物体。同样是研究，在功能空间和操作员空间上的线性异构体上生长了几个结果。 MON获得了Holomorthic曲线的Nevanlinna缺陷的消除理论，以用于PN（C），以实现有理运动目标。此外，他认为在holomorthic（或meromormormormorphic）映射的空间中引入了一个距离，并在该空间中获得了距离。然后，在没有nevanlinna缺陷的情况下，塑形（或层状）映射到PN（C）是密集的。 Itizuhara在某些奇异的积分操作员之间表现出换向器（B，T]的界限，以及…通过局部整合的功能Bon Morrey空间LPG（RN）具有一般增长功能G的更多乘法操作员，此结果部分地将经典结果推广到di Fazio和Ragusa引起的经典结果。以及作用于Riemann Sphere的不连续的群体，FATOU集合和朱莉亚集合riemarin Sphere的复杂动力学出现了，Kawamura使用了某些Ortanitial Onsological Onsopical of Toction todyn，则研究了一些混乱的特性。我们对拓扑动力学的研究与小波理论之间的关系。原田研究了关于有限环的编码理论的代数理论，并与有限环的编码与其他主题有关。较少的

项目成果

M.Kaneko (with E.Sato): "Notes on transference of continuity from maximal Fourier operators on Rn to those on Tn" Interdisplinary Information Sciences. vol.4. 97-107 (1998)

M.Kaneko（与 E.Sato）：“关于从 Rn 上的最大傅里叶算子到 Tn 上的最大傅里叶算子的连续性转移的注释”跨学科信息科学。

E.Sato: "On the Banach algebra M(p,q) (1≦p<q≦∞)" Tokyo J. of Math. 20. 219-240 (1997)

E.Sato：“论巴纳赫代数 M(p,q) (1≤p<q≤∞)”《东京数学杂志》20. 219-240 (1997)

M.Harada: "The euistence of a self-dual [70,35,12] code and for mally self-dual codes" Finite Filds and Thier Appl.3. 131-139 (1997)

M.Harada：“自对偶 [70,35,12] 代码的存在以及主要的自对偶代码”Finite Fields 和 Thier Appl.3。

S.Mori: "Elimination of defects of meromorphic mapping of C^m into P^n (C)" Ann.Acad.Sci.Fenn. (発表予定).

S.Mori：“C^m 亚态映射到 P^n (C) 的缺陷的消除”Ann.Acad.Sci.Fenn（待提交）。

S.Kawamura: "Covariant representations associated with chaotic dynamical systems" Tokyo T.of Math.20. 205-217 (1997)

S.Kawamura：“与混沌动力系统相关的协变表示”Tokyo T.of Math.20。