ハ-ディ空間と特異積分作用素に対する重み付きノルム不等式の研究

Hardy空间和奇异积分算子的加权范数不等式的研究

• 批准号: 07640251
• 负责人: 藤井 信彦
• 金额: --
• 依托单位: Tokai University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1995
• 资助国家: 日本
• 起止时间: 1995 至 无数据
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-07640251/
• 关键词: ハ-ディ空間; 特異積分作用素; ヒルベルト変換; 基底

今年度後半の主な研究題目としてL^2[-π,π)におおける基底の問題に取り組んだ.中村昭宏氏との討論において,基底の問題がweighted norm inequalityに関連することが分かり,その方面の問題を調べてみた.{λ_n}が互いに相異なる複素数からなる数列としたとき,Hruscev, Nikol'skii and Pavlovにより{e^<iλnx>}^∞_<n=-∞>がL^2〔-π,π)におけるunconditional basisあるいはRiesz basisをなすための条件としてCarlesonの条件およびL^2からHardy空間H^2へのToeplitz作用素の可逆性があげられていることを最近知った.Toeplitz作用素はHilbert変換がからみ,それはMuckenhouptのA_2条件,すなわちHelson-Szegoの条件に結びつき,Hruscev, Nruscev, Nikol'skii and Pavlovはそこを関数論的に議論を展開している.我々の研究の観点からすると,この議論を実解析的に跡付けることは非常に興味のあることであり,さらに関数論的な立場から議論されたweighted norm inequalityの問題を考えなおすという見地に今までの議論では欠落していた情報をもたらすことが期待でき,いくつかの項目の新たなつながりを見出す可能性があると考えられる.また,本来の,指数関数系{e^<iλnx>}^∞_<n=-∞>の基底の問題にも新たなアプローチの方法を提供できるのではと考えている。我々はこの観点から中村昭宏氏(東海大開発工学部)との共同研究において実数例{λ_n}において,指数関数系{e^<iλnx>}^∞_<n=-∞>がminimal(1次独立性に相当する性質)になるための1つの十分条件を得ている.これは‘Exponential Systemのminimal性について'と題し1995年10月の福島大における‘実解析セミナー'において発表し,1996年4月の日本数学会年会実函数論文科会において中村昭宏氏との連名で発表予定である.

The main research topic in the second half of this year is L^2 [-π, π]. Akira Nakamura's discussion on the basis of the problem is related to the weighted norm quality, and the problem of the other aspects is discussed. {λ_n}{λ_n}{λ_n} A discussion on the number theory is developed in this paper, which is based on Muckenhoupt's A_2 condition, Helson-Szego condition, Hruscev, Nruscev, Nikol 'skii and Pavlov. The research points of this paper are as follows: (1) the research points of this paper are as follows: (2) the research points of this paper are as follows: (3) the research points of this paper are as follows: (4) the research points of this paper are as follows: (5) the research points of this paper are as follows: (6) the research points of this paper are as follows: (7) the research points of this paper are as follows: (8) the research points of this paper are as follows: (9) the research points of this paper are as follows: (1) the research points of this paper are as follows: (1) the research points of this paper are as follows: (2) the research points of this paper are as follows: (1) the research points of this paper is as follows: (2) the research points of this paper is as follows: (3) the research points of this paper is as follows: (4) the research points of this paper is as follows: (5) the research points of this paper is as follows: (4) the research points of this paper is as follows: (5) the research points For the basic problem of exponential relationship {e ^<i λ nx>}^∞_<n =-∞>, a new method is provided. Akihiro Nakamura (Department of Engineering, Tokai University) and I jointly studied the exponential relationship system {e ^<i λ nx>}^∞_<n =-∞> for minimal (1st degree independence, equivalent property). The topic of "minimal property of Exponential System" was proposed at Fukushima University in October 1995, and the topic of "practical analysis" was proposed at the annual meeting of Japanese Mathematical Society in April 1996.