Characterizations of real Hardy spaces and functional analysis

真实 Hardy 空间的表征和泛函分析

基本信息

  • 批准号:
    13640148
  • 负责人:
  • 金额:
    $ 2.18万
  • 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:
    2001
  • 资助国家:
    日本
  • 起止时间:
    2001 至 2003
  • 项目状态:
    已结题

项目摘要

We have been interesting in the methods to judge whether a given tempered distribution f on n-dimensional Euclidean space is in a Hardy space or not. One of the methods is to investigate the integrability of one of the maximal functions made from f. There are many kinds of maximal functions which might be the tools for the purpose. Among them, we have picked up the following maximal functions. We take a test function on the same space where f is given and consider the dilations of it with dilation rates t. Then we have a family of the functions which are the convolutions of f and the dilations of the test function with the dilation rates t. Then the components of the family have parameters t. The vertical maximal function of f with respect to the given test function is defined by the supremum of the family taken over all t > 0. The non-tangential maximal function is such a function whose value at a point x is the supremum of the values of the convolution over such t and y that the dist … More ance from x to y is in less than t. The modified maximal function is the improvement of the non-tangential maximal function to reflect the behavior of the convolution in the long distant area from x. The above maximal functions are determined by the given test function. Now we consider the all test functions satisfying certain conditions. For each test function, we can get a corresponding vertical maximal function. Among them we take the largest one and call it the grand maximal function of f. We have also treated the vertical maximal function and the non-tangential maximal function made from the Poisson integral of f.In our research, we have investigated the integral estimates of such functions that are obtained by putting a function of lower p type over the above maximal functions. These integrals contain the Orlicz-norms and the p-th integral means.We have proved the equivalence between the finiteness of these integrals and given some improvements of proofs appearing in the papers treating the related topics. Less
We have been interesting in the methods to judge whether a given tempered distribution f on n-dimensional Euclidean space is in a Hardy space or not. One of the methods is to investigate the integrability of one of the maximal functions made from f. There are many kinds of maximal functions which might be the tools for the purpose. Among them, we have picked up the following maximal functions. We take a test function on the same space where f is given and consider the dilations of it with dilation rates t. Then we have a family of the functions which are the convolutions of f and the dilations of the test function with the dilation rates t. Then the components of the family have parameters t. The vertical maximal function of f with respect to the given test function is defined by the supremum of the family taken over all t > 0. The non-tangential maximal function is such a function whose value at a point x is the supremum of the values of the convolution over such t and y that the dist … More ance from x to y is in less than t. The modified maximal function is the improvement of the non-tangential maximal function to reflect the behavior of the convolution in the long distant area from x. The above maximal functions are determined by the given test function. Now we consider the all test functions satisfying certain conditions. For each test function, we can get a corresponding vertical maximal function. Among them we take the largest one and call it the grand maximal function of f. We have also treated the vertical maximal function and the non-tangential maximal function made from the Poisson integral of f.In our research, we have investigated the integral estimates of such functions that are obtained by putting a function of lower p type over the above maximal functions. These integrals contain the Orlicz-norms and the p-th integral means.We have proved the equivalence between the finiteness of these integrals and given some improvements of proofs appearing in the papers treating the related topics. Less

项目成果

期刊论文数量(29)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
田谷久雄, 福田隆: "岩澤不変量の計算"日本応用数理学会論文誌. 12 4. 293-306 (2002)
Hisao Taya,Takashi Fukuda:“岩泽不变量的计算”日本应用数学学会杂志 12 4. 293-306 (2002)。
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  • 影响因子:
    0
  • 作者:
  • 通讯作者:
F.Hiai: "Concavity of certain matrix trace functions"Taiwan J. Math.. 5・3. 535-554 (2001)
F.Hiai:“某些矩阵迹函数的凹性”台湾 J. Math.. 5・3(2001)
  • DOI:
  • 发表时间:
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  • 影响因子:
    0
  • 作者:
  • 通讯作者:
F.Hiai, M.Miguo, D.Petg: "Free relative entropy for measures and a corresponding perturbation theory"J.Math.Soc.Japan. 54・3. 679-718 (2002)
F.Hiai、M.Miguo、D.Petg:“测度的自由相对熵和相应的微扰理论”J.Math.Soc.Japan 54・3(2002)。
  • DOI:
  • 发表时间:
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  • 影响因子:
    0
  • 作者:
  • 通讯作者:
M.Nakamura, T.Ogawa: "Small solutions to nonlinear wave equations in the sobolev spaces"Houston J. Math.. 27・3. 613-632 (2001)
M.Nakamura、T.Okawa:“索博列夫空间中非线性波动方程的小解”Houston J. Math.. 27・3(2001)。
  • DOI:
  • 发表时间:
  • 期刊:
  • 影响因子:
    0
  • 作者:
  • 通讯作者:
田谷 久雄, 福田 隆: "岩澤不変量の計算"日本応用数理学会論文誌. 12・4. 293-306 (2002)
Hisao Taya,Takashi Fukuda:“岩泽不变量的计算”日本应用数学学会杂志12・4(2002)。
  • DOI:
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  • 期刊:
  • 影响因子:
    0
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KANEKO Makoto其他文献

KANEKO Makoto的其他文献

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{{ truncateString('KANEKO Makoto', 18)}}的其他基金

The semantics and pragmatics of Japanese plurals
日语复数的语义和语用
  • 批准号:
    23520463
  • 财政年份:
    2011
  • 资助金额:
    $ 2.18万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Challenge of real time stiffness measurement of red blood cells
红细胞实时硬度测量的挑战
  • 批准号:
    23656186
  • 财政年份:
    2011
  • 资助金额:
    $ 2.18万
  • 项目类别:
    Grant-in-Aid for Challenging Exploratory Research
Assessment of the efficacy of collagen-coated-bead columns for antiplatelet therapy in clinical settings
评估临床环境中胶原蛋白涂层珠柱抗血小板治疗的功效
  • 批准号:
    21790532
  • 财政年份:
    2009
  • 资助金额:
    $ 2.18万
  • 项目类别:
    Grant-in-Aid for Young Scientists (B)
Analysis of the Mechanism of the Delay Characteristics in Cornea Deformation of Living Eye
活体眼角膜变形延迟特性机制分析
  • 批准号:
    19300183
  • 财政年份:
    2007
  • 资助金额:
    $ 2.18万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
A study of constructions in Japanese and in French including a negative polarity item and conveying a surprise or an exclamation
对日语和法语结构的研究,包括负极性项目并表达惊讶或感叹
  • 批准号:
    19520346
  • 财政年份:
    2007
  • 资助金额:
    $ 2.18万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Non-Contact Stiffness Imager
非接触式刚度成像仪
  • 批准号:
    17360116
  • 财政年份:
    2005
  • 资助金额:
    $ 2.18万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
Research on Tactile Differentiator
触觉区分器的研究
  • 批准号:
    14350132
  • 财政年份:
    2002
  • 资助金额:
    $ 2.18万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
Tracing Type Active Antenna with Friction Independence
具有摩擦无关性的跟踪型有源天线
  • 批准号:
    12650251
  • 财政年份:
    2000
  • 资助金额:
    $ 2.18万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Grasp strategy for pyramidal-like object
金字塔状物体的抓取策略
  • 批准号:
    10650259
  • 财政年份:
    1998
  • 资助金额:
    $ 2.18万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Studies on Hardy spaces by real analytic methods
Hardy空间的实解析方法研究
  • 批准号:
    09640146
  • 财政年份:
    1997
  • 资助金额:
    $ 2.18万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
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