A study of harmonic analysis for orthogonal expansions

正交展开的调和分析研究

基本信息

  • 批准号:
    17540155
  • 负责人:
  • 金额:
    $ 1.98万
  • 依托单位:
  • 依托单位国家:
    日本
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
  • 财政年份:
    2005
  • 资助国家:
    日本
  • 起止时间:
    2005 至 2006
  • 项目状态:
    已结题

项目摘要

Our main results of this research project are summarized as follows. The transplantation theorem for the Hankel transform has been proved on the real Hardy space. A transplantation operator is an operator which maps a function with the Fourier expansion in an orthogonal system to the function with the same Fourier coefficients with respect to another orthogonal system. A transplantation theorem is a theorem which asserts the boundedness of the transplantation operator. This type of theorem is a useful tool in harmonic analysis for orthogonal expansions. The Hankel transform is one of the integral transforms, and coincides with the Fourier transform as a special case. Estimations of operators on the real Hardy space allow us to get the corresponding estimations of the operators on the Lebesegue spaces. In such a useful scheme, we have obtained a transplantation theorem.Transplantation operators are regarded as a generalization of the Hilbert transform. It is known that the Hilbert transform maps a function with certain conditions to an integrable function. We have proved that the transplantation operators for the Hankel transform have the same properties. Using this result, we have showed that the Cesaro operators for the Hankel transform are bounded on the space of integrable functions and on the real Hardy space.We have obtained Paley's inequality of integral transform type. The classical Paley inequality says that in the Fourier expansion of a function in the real Hardy space, the sum of the absolute values of its Fourier coefficients taken over the Hadamard gaps converges, and the sum is bounded by the square of the real Hardy space norm of the function. We have showed that an inequality of the same type as the classical Paley inequality holds for the Hankel transform.
我们的研究项目的主要结果总结如下。汉克尔变换的移植定理已在真实的空间上得到了证明。移植运算符是一个运算符,可将正交系统中傅立叶扩展的函数映射到与另一个正交系统相同的傅立叶系数的函数。移植定理是一个定理,它主张移植算子的界限。这种类型的定理是用于正交扩展的谐波分析中的有用工具。 Hankel变换是整体变换之一,与傅立叶变换作为特殊情况相吻合。对实际耐力空间的运营商的估计使我们能够在Lebesegue空间上获得对操作员的相应估计。在这样有用的方案中,我们获得了移植定理。移植算子被认为是希尔伯特变换的概括。众所周知,希尔伯特变换将具有某些条件的函数映射到可集成的函数。我们已经证明,Hankel变换的移植操作员具有相同的属性。使用此结果,我们表明,汉克尔变换的塞萨罗运算符在可集成函数和实际耐寒空间的空间上有界。我们获得了Paley对整体变换类型的不平等。经典的Paley不平等说明,在实际强度空间中功能的傅立叶扩展中,其傅立叶系数的绝对值之和在Hadamard Gaps上收敛,总和由真实强壮空间的正方形界定功能。我们已经表明,与经典的Paley不等式相同类型的不等式对于Hankel变换而言。

项目成果

期刊论文数量(17)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
A nonlinear model of visual information processing based on discrete maximal overlap wavelets
基于离散最大重叠小波的视觉信息处理非线性模型
  • DOI:
  • 发表时间:
    2005
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Dieter Kotschick;Shigeyuki Morita;堤 幸太;Mitsuteru Inoue;山田宗慶;Toshiya JIMBO;中橋孝博・飯塚勝;桐原 聡秀;Hitoshi Arai
  • 通讯作者:
    Hitoshi Arai
Harmonic analysis for orthogonal expansions
正交展开的调和分析
  • DOI:
  • 发表时间:
    2006
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Akihiko;Miyachi;Yuichi Kanjin
  • 通讯作者:
    Yuichi Kanjin
Uniqueness theorems in an angular domain
  • DOI:
    10.2748/tmj/1170347687
  • 发表时间:
    2006-12-01
  • 期刊:
  • 影响因子:
    0.5
  • 作者:
    Lin, Weichuan;Mori, Seiki;Tohge, Kazuya
  • 通讯作者:
    Tohge, Kazuya
Singular and fractional integrals along variable surfaces
  • DOI:
    10.14492/hokmj/1285766308
  • 发表时间:
    2006
  • 期刊:
  • 影响因子:
    0.5
  • 作者:
    D. Fan;Shuichi Sato
  • 通讯作者:
    D. Fan;Shuichi Sato
Weighted estimates for maximal functions associated with Fourier multipliers
与傅里叶乘数相关的最大函数的加权估计
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KANJIN Yuichi其他文献

KANJIN Yuichi的其他文献

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{{ truncateString('KANJIN Yuichi', 18)}}的其他基金

A study of harmonic analysis in orthogonal expansions
正交展开中的调和分析研究
  • 批准号:
    21540170
  • 财政年份:
    2009
  • 资助金额:
    $ 1.98万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
A study of harmonic analysis in orthogonal expansions
正交展开中的调和分析研究
  • 批准号:
    19540172
  • 财政年份:
    2007
  • 资助金额:
    $ 1.98万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Harmonic Analysis for Orthogonal Expansions
正交展开式的调和分析
  • 批准号:
    15540161
  • 财政年份:
    2003
  • 资助金额:
    $ 1.98万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Harmonic Analysis for Some Orthogonal Expansions
一些正交展开的调和分析
  • 批准号:
    13640160
  • 财政年份:
    2001
  • 资助金额:
    $ 1.98万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Harmonic Analysis on Orthogonal Expansions
正交展开式的调和分析
  • 批准号:
    10640155
  • 财政年份:
    1998
  • 资助金额:
    $ 1.98万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)

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Investigation of Inverse Problems for the Heat equation Based on the Theory of Stochastic Control
基于随机控制理论的热方程反问题研究
  • 批准号:
    16540100
  • 财政年份:
    2004
  • 资助金额:
    $ 1.98万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Harmonic Analysis for Orthogonal Expansions
正交展开式的调和分析
  • 批准号:
    15540161
  • 财政年份:
    2003
  • 资助金额:
    $ 1.98万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
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