2007 Fiscal Year Final Research Report Summary
HARMONIC ANALYSIS IN THE OPERATORS OF THE FUNCTION SPACES RELATED TO THE ORTHOGONAL SYSTEMS
| Project/Area Number |
18540157
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Yamagata University |
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Principal Investigator |
SATO Enji Yamagata University, FACULTY OF SCIENCE, PROFESSOR (80107177)
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| Co-Investigator(Kenkyū-buntansha) |
MORI Seiki Yamagata University, FACULTY OF SCIENCE, PROFESSOR (80004456)
MIZUHARA Takahiro Yamagata University, FACULTY OF SCIENCE, PROFESSOR (80006577)
KAWAMURA Shinzo Yamagata University, FACULTY OF SCIENCE, PROFESSOR (50007176)
KANJIN Yuichi Kanazawa University, FACULTY DIVISION OF INNOVATIVE TECHNOLOGY AND SCIENCE GRADUATE SCHOOL OF NATURAL SCIENCE AND TECHNOLOGY PROFESSOR, PROFESSOR (50091674)
MIYACHI Akihiko TOKYO WOMANS CHRISTIAN UNIVERSITY, DEPARTMENT OF MATBEMATICS, PROFESSOR (60107696)
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| Project Period (FY) |
2006 – 2007
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| Keywords | Hankel transform / Lorentz-Zvemund spaces / value distribuntion theory / uniauness thorem / Morrev spaces / chaotic system / transplantation theorem / weighted Hardy spaces |
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| Research Abstract |
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 follows
Sato 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
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[Presentation] 移植作用素とチェザロ作用素2007
Author(s)
勘甚裕一
Organizer
第46回実関数論・関数解析合同シンポジュウム
Place of Presentation
九州大学西新プラザ
Year and Date
2007-08-08
Description
「研究成果報告書概要(和文)」より
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[Presentation] The devil step and a strange slope2006
Author(s)
Shinzo Kawamura and Hongqing Wang
Organizer
Conference(Study of the structure in Banach space and function space)
Place of Presentation
Research Iinstitute for Mathermatical Sciences, Kyoto University
Year and Date
20060607-09
Description
「研究成果報告書概要(欧文)」より
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