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Study of singular integrals and function spaces

Research Project

Project/Area Number 19540198
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionTokai University

Principal Investigator

KOMORI Yasuo  Tokai University, 開発工学部, 准教授 (70234903)

Co-Investigator(Kenkyū-buntansha) 水原 昴廣  山形大学, 理学部, 教授 (80006577)
中井 英一  大阪教育大学, 教育学部, 教授 (60259900)
立澤 一哉  北海道大学, 理学研究院, 准教授 (80227090)
Co-Investigator(Renkei-kenkyūsha) 水原 昴廣  山形大学, 理学部, 教授 (80006577)
中井 英一  大阪教育大学, 教育学部, 教授 (60259900)
立澤 一哉  北海道大学, 理学研究院, 准教授 (80227090)
Project Period (FY) 2007 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords特異積分 / ハーディー空間 / BMO / ヘルツ空間 / 重みつき評価
Research Abstract

一般化された特異積分作用素のハーディー空間上での有界性について研究を進め, コーシー積分作用素とn次元のカルデロンの交換子作用素がハーディー空間から局所ハーディー空間への有界作用素であること, その結果が最良であることを示した

Report

(3 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • Research Products

    (42 results)

All 2009 2008 2007 2006

All Journal Article (13 results) (of which Peer Reviewed: 13 results) Presentation (29 results)

  • [Journal Article] Weighted Morrey spaces and a singular integral operator2009

    • Author(s)
      Yasuo Komori and Satoru Shirai
    • Journal Title

      Math. Nachrichten vol.282

      Pages: 219-231

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Weighted Morrey spaces and a singular integral operator2009

    • Author(s)
      Yasuo Komori
    • Journal Title

      Math. Nachrichten 282

      Pages: 219-231

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Cauchy integral operators on Hardy spaces2008

    • Author(s)
      Yasuo Komori
    • Journal Title

      Hokkaido Math. J. vol.37

      Pages: 389-398

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Calderon's commutator on H^p(R^n)2008

    • Author(s)
      Yasuo Komori
    • Journal Title

      International J. of Pure and Applied Math. vol.47

      Pages: 225-234

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A generalization of Hardy spaces H^p by using atoms2008

    • Author(s)
      Eiichi Nakai
    • Journal Title

      Acta Mathematica Sinica vol.24

      Pages: 1243-1268

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] An elementary proof of Sobolev embeddings for Riesz potentials of functions in Morrey spaces L^{1, ν, β}(G)2008

    • Author(s)
      Yoshihiro Mizuta, Eiichi Nakai, Takao Ohno and Tetsu Shimomura
    • Journal Title

      Hiroshima Mathematical Journal vol.38

      Pages: 425-436

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Orlicz-Morrey spaces and the Hardy-Littlewood maximal function2008

    • Author(s)
      Eiichi Nakai
    • Journal Title

      Studia Mathematica vol.188

      Pages: 193-221

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Wavelet characterizations of weighted Herz spaces2008

    • Author(s)
      Izuki Mitsuo and Tachizawa Kazuya
    • Journal Title

      Sci. Math. Jpn. vol.67

      Pages: 353-363

    • NAID

      10021089666

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Cauchy integral operators on Hardy spaces2008

    • Author(s)
      Yasuo Komori
    • Journal Title

      Hokkaido Math. J. 37

      Pages: 389-398

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Calderon's commutator on H^p(R^n)2008

    • Author(s)
      Yasuo Komori
    • Journal Title

      International J. of Pure and Applied Math. 47

      Pages: 225-234

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Calderon-Zygmund operators on amalgam spaces and in the discrete case2007

    • Author(s)
      Norio Kikuchi, Eiichi Nakai, Naohito Tomita, Kozo Yabuta and Tsuyoshi Yoneda
    • Journal Title

      J. of Math. Analysis and Applications vol.335

      Pages: 198-212

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Calderon-Zygmund operators on amalgam spaces and in the discrete case2007

    • Author(s)
      中井 英一
    • Journal Title

      J. Math. Anal. and Appl. 335

      Pages: 198-212

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Construction of an atomic decomposition for functions with compact support2006

    • Author(s)
      Eiichi Nakai
    • Journal Title

      J. of Math. Analysis and Applications Vol.313

      Pages: 730-737

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Presentation] Singular and fractional integral operators on predual of Campanato spaces2009

    • Author(s)
      中井英一
    • Organizer
      日本数学会年会
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-26
    • Related Report
      2008 Final Research Report
  • [Presentation] Real-variable methods in harmonic analysis2009

    • Author(s)
      小森康雄
    • Organizer
      発展方程式シンポジウム
    • Place of Presentation
      東海大学
    • Year and Date
      2009-03-11
    • Related Report
      2008 Annual Research Report 2008 Final Research Report
  • [Presentation] Div-Curl lemmaとその周辺2008

    • Author(s)
      小森康雄
    • Organizer
      調和解析セミナー
    • Place of Presentation
      山形大学
    • Year and Date
      2008-12-23
    • Related Report
      2008 Final Research Report
  • [Presentation] Some weak estimates for singular integral operators on Herz spaces2008

    • Author(s)
      小森康雄, 松岡勝男
    • Organizer
      実解析学シンポジウム
    • Place of Presentation
      山口大学
    • Year and Date
      2008-11-08
    • Related Report
      2008 Final Research Report
  • [Presentation] Singular integrals on generalized Hardy spaces2008

    • Author(s)
      中井英一
    • Organizer
      実解析学シンポジウム
    • Place of Presentation
      山口大学
    • Year and Date
      2008-11-08
    • Related Report
      2008 Final Research Report
  • [Presentation] Some weak estimate for singular integral operators on Herz spaces2008

    • Author(s)
      小森康雄
    • Organizer
      実解析学シンポジウム
    • Place of Presentation
      山口大学
    • Year and Date
      2008-11-08
    • Related Report
      2008 Annual Research Report
  • [Presentation] Pseudo-differential operators on Hardy spaces2008

    • Author(s)
      Yasuo Komori
    • Organizer
      Harmonic Analysis and its Applications
    • Place of Presentation
      Tokyo Metropolitan Univ.
    • Year and Date
      2008-10-12
    • Related Report
      2008 Final Research Report
  • [Presentation] Pseudo-differential operators on Hardy spaces2008

    • Author(s)
      Yasuo Komori
    • Organizer
      Harmonic Analysis and its Applications
    • Place of Presentation
      Tokyo Metropolitan University
    • Year and Date
      2008-10-12
    • Related Report
      2008 Annual Research Report
  • [Presentation] A generalization of Hardy spaces by using atoms and fractional integrals2008

    • Author(s)
      Eiichi Nakai
    • Organizer
      Harmonic Analysis and its Applications
    • Place of Presentation
      Tokyo Metropolitan Univ
    • Year and Date
      2008-10-10
    • Related Report
      2008 Final Research Report
  • [Presentation] Boundedness of fractional integral operators on Morrey spaces and Sobolev embeddings for generalized Riesz potentials2008

    • Author(s)
      水田義弘, 中井英一, 大野貴雄, 下村哲
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-24
    • Related Report
      2008 Final Research Report
  • [Presentation] An elementary proof of Soboleb embeddings for Riesz potentials of functions in L^1 Morrey spaces2008

    • Author(s)
      Yoshihiro Mizuta, Eiichi Nakai, Takao Ohno and Tetsu Shimomura
    • Organizer
      The Eleventh Conference on Real and Complex Analysis (日韓共同 実・複素解析セミナー)
    • Place of Presentation
      Hiroshima Univ.
    • Year and Date
      2008-09-18
    • Related Report
      2008 Final Research Report
  • [Presentation] A generalization of Hardy spaces and fractional integrals2008

    • Author(s)
      Eiichi Nakai
    • Organizer
      International Workshop on Interpolation Theory, Function Spaces and Related Topics
    • Place of Presentation
      Toledo(Spain)
    • Year and Date
      2008-09-07
    • Related Report
      2008 Final Research Report
  • [Presentation] A generalization of Hardy spaces by using atoms2008

    • Author(s)
      Eiichi Nakai
    • Organizer
      International Workshop on Function Spaces and Applications
    • Place of Presentation
      Freyburg/Unstrut(Germany)
    • Year and Date
      2008-07-06
    • Related Report
      2008 Final Research Report
  • [Presentation] A generalization of Hardy spaces on spaces of homogeneous type2008

    • Author(s)
      中井英一
    • Organizer
      研究集会「バナッハ空間及び関数空間論の最近の進展とその応用」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2008-06-04
    • Related Report
      2008 Final Research Report
  • [Presentation] Time-Frequency解析, Dyadic解析入門2007

    • Author(s)
      小森康雄
    • Organizer
      調和解析セミナー
    • Place of Presentation
      草津セミナーハウス
    • Year and Date
      2007-12-23
    • Related Report
      2008 Final Research Report
  • [Presentation] H^p and Lip_α2007

    • Author(s)
      中井英一
    • Organizer
      実解析学シンポジウム
    • Place of Presentation
      大阪教育大学天王寺キャンパス
    • Year and Date
      2007-10-20
    • Related Report
      2008 Final Research Report
  • [Presentation] 一般化Morrey-Campanato空間の前相対空間2007

    • Author(s)
      中井英一
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東北大学川内北キャンパス
    • Year and Date
      2007-09-21
    • Related Report
      2008 Final Research Report
  • [Presentation] 一般化Morrey-Campanato空間の前相対空間2007

    • Author(s)
      中井 英一
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-21
    • Related Report
      2007 Annual Research Report
  • [Presentation] Preduals of generalized Morrey-Campanato spaces2007

    • Author(s)
      Eiichi Nakai
    • Organizer
      Harmonic Analysis and its Applications at Sapporo
    • Place of Presentation
      Hokkaido Univ
    • Year and Date
      2007-09-02
    • Related Report
      2008 Final Research Report
  • [Presentation] Preduals of Morrey-Campanato spaces2007

    • Author(s)
      Eiichi Nakai
    • Organizer
      研究集会「バナッハ空間、関数空間及び不等式の研究とその応用 (Banach spaces, function spaces, inequalities and their applications)」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-06-06
    • Related Report
      2008 Final Research Report
  • [Presentation] f'(x)=4f(2x)の解の表示式の構造及びその数値計算について2007

    • Author(s)
      米田剛, 中井英一
    • Organizer
      日本数学会年会
    • Place of Presentation
      埼玉大学理学部
    • Year and Date
      2007-03-27
    • Related Report
      2008 Final Research Report
  • [Presentation] Construction of solutions for the functional-differential equation $f'(x)=a f(\lambda x)$, $\lambda>1$2007

    • Author(s)
      Eiichi Nakai and Tsuyoshi Yoneda
    • Organizer
      Harmonic Analysis and its Applications at Tokyo
    • Place of Presentation
      Tokyo Woman's Christian Univ.
    • Year and Date
      2007-03-24
    • Related Report
      2008 Final Research Report
  • [Presentation] On the weighted Herz spaces and the boundedness for some sublinear operatos2006

    • Author(s)
      小森康雄, 松岡勝男
    • Organizer
      調和解析セミナー
    • Place of Presentation
      大阪教育大学
    • Year and Date
      2006-12-24
    • Related Report
      2008 Final Research Report
  • [Presentation] 特性関数における多変数フーリエ級数の各点収束について2006

    • Author(s)
      大坪和弥, 倉坪茂彦, 中井英一
    • Organizer
      実解析学シンポジウム
    • Place of Presentation
      弘前大学理工学部
    • Year and Date
      2006-10-28
    • Related Report
      2008 Final Research Report
  • [Presentation] 特性関数の多変数フーリエ級数におけるピンスキー現象について2006

    • Author(s)
      大坪和弥, 倉坪茂彦, 中井英一
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      大阪市立大学杉本キャンパス
    • Year and Date
      2006-09-19
    • Related Report
      2008 Final Research Report
  • [Presentation] Weighted Morrey space and maximal operator2006

    • Author(s)
      小森康雄, 白井悟
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      大阪市立大学 杉本キャンパス
    • Year and Date
      2006-09-19
    • Related Report
      2008 Final Research Report
  • [Presentation] Singular integral operators on Orlicz-Morrey spaces2006

    • Author(s)
      Eiichi Nakai
    • Organizer
      The Second International Symposium on BANACH and FUNCTION SPACES
    • Place of Presentation
      Kyushu Institute of Technology
    • Year and Date
      2006-09-14
    • Related Report
      2008 Final Research Report
  • [Presentation] Singular integral operators on H^p(R^n)2006

    • Author(s)
      小森康雄
    • Organizer
      調和解析と非線形偏微分方程式
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2006-07-07
    • Related Report
      2008 Final Research Report
  • [Presentation] On Orlicz-Morrey spaces2006

    • Author(s)
      中井英一
    • Organizer
      研究集会「バナッハ空間及び関数空間の構造の研究」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2006-06-07
    • Related Report
      2008 Final Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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