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A study of harmonic analysis in orthogonal expansions

Research Project

Project/Area Number 21540170
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

KANJIN Yuichi  金沢大学, 機械工学系, 教授 (50091674)

Co-Investigator(Kenkyū-buntansha) SATO Shuichi  金沢大学, 学校教育系, 准教授 (20162430)
Co-Investigator(Renkei-kenkyūsha) TOHGE Kazuya  金沢大学, 電子情報系, 准教授 (30260558)
ARAI Hitosi  東京大学, 大学院・数理科学研究科, 教授 (10175953)
MIYACHI Akihiko  東京女子大学, 現代教養学部, 教授 (60107696)
Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywordsハーディの不等式 / ペーリーの不等式 / 実ハーディ空間 / ラゲール展開 / エルミート展開 / ハンケル変換 / メーラー変換
Research Abstract

We have obtained Hardy type inequalities for the Hermite expansion, the Laguerre expansions and the Mehler transforms, which are analogues of the classical Hardy inequality on the Hardy space. For Hermite and Laguerre expansions, the inequalities hold on the space of integrable functions. Also, the Paley type inequality for the Hankel transform has been obtained. Moreover, we have showed that the functions with positive Laguerre coefficients have the property that local square integrability at the origin implies global square integrability.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (33 results)

All 2012 2011 2010 2009 Other

All Journal Article (20 results) (of which Peer Reviewed: 20 results) Presentation (7 results) Remarks (6 results)

  • [Journal Article] Schatten p-class property of pseudo-differencial operators with symbols in modulation spaces2012

    • Author(s)
      Kobayasi, M., Miyachi, A.
    • Journal Title

      Nagoya Math. J.

      Volume: 205 Pages: 119-148

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Hardy's inequalities for Hermite and Laguerre ezpansions revisited2011

    • Author(s)
      Kanjin, Y.
    • Journal Title

      J. Math. Soc. Japan

      Volume: 63 Pages: 753-767

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Onweighted weak type norm inequalitiesfor one-sided oscillatory singularintegrals2011

    • Author(s)
      Fu, Z., Lu, S., Sato, S., Shi, S.
    • Journal Title

      Studia Math

      Volume: 207 Pages: 137-151

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Weak-type(1, 1) estimates for parabolic singular integrals2011

    • Author(s)
      Sato, S.
    • Journal Title

      Proc. Edinb. Math. Soc., II

      Volume: 54, No.1 Pages: 221-247

    • NAID

      120003628224

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Refinements of the Hardy and Morgan uncertainty principles2011

    • Author(s)
      Kawazoe, T., Liu, J., Miyachi, A.
    • Journal Title

      Scientiae Mathematicae Japonicae

      Volume: 73 Pages: 81-87

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Tropical Nevanlinna theory and second main theorem2011

    • Author(s)
      Laine, I., Thoge, K.
    • Journal Title

      Proc. London Math. Soc.

      Volume: 102 Pages: 1-40

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] A unit disc analogue of the Bank-Laine conjecture does not hold2011

    • Author(s)
      Heittokangas, J., Thoge, K.
    • Journal Title

      Ann. Acad. Sci. Fenn. Math.

      Volume: 36 Pages: 341-351

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Hardy's inequalities for Hermite and Laguerre expansions revisited2011

    • Author(s)
      Yuichi Kanjin
    • Journal Title

      J.Math.Soc.Japan

      Volume: 63 Pages: 753-767

    • NAID

      10029321824

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Weak type (1,1) estimates for parabolic singular integrals2011

    • Author(s)
      Shuichi Sato
    • Journal Title

      Proc.Edinb.Math.Soc., II.Ser.

      Volume: 54 Pages: 221-247

    • NAID

      120003628224

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On Gundersen's solution to the Fermat-type functional equation of degree 62010

    • Author(s)
      Tohge, K.
    • Journal Title

      Complex Variables and Elliptic Equations

      Volume: 56 Pages: 233-251

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Hardy's inequalities for Hermite and Laguerre expansions revisited2010

    • Author(s)
      Yuichi Kanjin
    • Journal Title

      J.Math.Soc.Japan (in press)

    • NAID

      10029321824

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Weak type (1, 1) estimates for parabolic singular integrals2010

    • Author(s)
      Shuichi Sato
    • Journal Title

      Proc.Edinb.Math.Soc. (in press)

    • NAID

      120003628224

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Paley's inequality of integral transform type2009

    • Author(s)
      Kanjin, Y., Sato, K.
    • Journal Title

      Hokkaido Math. J.

      Volume: 38 Pages: 233-247

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Estimates for singular integrals along surfaces of revolution2009

    • Author(s)
      Sato, S.
    • Journal Title

      J. Aust. Math. Soc.

      Volume: 86 Pages: 413-430

    • NAID

      120001643237

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Embedding relations between local Hardy and modulation spaces2009

    • Author(s)
      Kobayashi, M., Miyachi, A., Tomita, N.
    • Journal Title

      Studia Math.

      Volume: 192 Pages: 79-96

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Boundedness of the Hausdorff operators in Hp spaces2009

    • Author(s)
      Liflyand, E., Miyachi, A.
    • Journal Title

      Studia Mat h.

      Volume: 194 Pages: 279-292

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Paley's inequality of integral transform type2009

    • Author(s)
      Yuichi Kanjin, Kunio Sato
    • Journal Title

      Hokkaido Math.J. 38

      Pages: 233-247

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Nonisotropic dilations and the method of rotations with weight

    • Author(s)
      Sato, S.
    • Journal Title

      Proc. Amer. Math. Soc.

      Volume: (in press)

    • NAID

      120004140843

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On logarithmic order of an entire function in terms of the coefficients

    • Author(s)
      Ishizaki, K., Thoge, K.
    • Journal Title

      Proc. Amer. Math. Soc.

      Volume: (in press)

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Hardy's inequalities for Hermite and Laguerre expansions revisited

    • Author(s)
      Yuichi Kanjin
    • Journal Title

      J.Math.Soc.Japan

      Volume: in press

    • NAID

      10029321824

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] Sharp smoothness conditions for bilinear Fourier multipliers2012

    • Author(s)
      冨田直人,宮地晶彦
    • Organizer
      日本数学会年会実関数論分科会
    • Place of Presentation
      東京理科大学神楽坂キャンパス(東京都)
    • Year and Date
      2012-03-29
    • Related Report
      2011 Final Research Report
  • [Presentation] On logarithmic order of an entire function in terms of the coefficients2012

    • Author(s)
      藤解和也
    • Organizer
      日本数学会年会実関数論分科会
    • Place of Presentation
      東京理科大学神楽坂キャンパス(東京都)
    • Year and Date
      2012-03-26
    • Related Report
      2011 Final Research Report
  • [Presentation] Some non-regular convolution operators2010

    • Author(s)
      佐藤秀一
    • Organizer
      日本数学会総合分科会実関数論分科会特別講演
    • Place of Presentation
      名古屋大学(愛知県)
    • Year and Date
      2010-09-24
    • Related Report
      2011 Final Research Report
  • [Presentation] Tropical Nevanlinna theory in a single variable2010

    • Author(s)
      Tohge, K.
    • Organizer
      Workshop on Function Theory and Dynamical Systems
    • Place of Presentation
      University College London(GB)
    • Year and Date
      2010-09-08
    • Related Report
      2011 Final Research Report
  • [Presentation] Transplantation theorems for orthogonal expansions2009

    • Author(s)
      Kanjin, Y.
    • Organizer
      Harmonic Analysis and its Applications at Pohang 2009
    • Place of Presentation
      浦項工科大学(韓国)
    • Year and Date
      2009-11-26
    • Related Report
      2011 Final Research Report
  • [Presentation] Transplantation theorems for orthogonal expansions2009

    • Author(s)
      Yuichi Kanjin
    • Organizer
      Harmonic Analysis and its applications at Pohang 2009
    • Place of Presentation
      浦項工科大学 (韓国)
    • Year and Date
      2009-11-26
    • Related Report
      2009 Annual Research Report
  • [Presentation] Change of variables for weighted Hardy spaces on a domain2009

    • Author(s)
      Miyachi, A.
    • Organizer
      Harmonic Analysis and Partial Differential Equations
    • Place of Presentation
      北京師範大学(中国)
    • Year and Date
      2009-05-28
    • Related Report
      2011 Final Research Report
  • [Remarks]

    • URL

      http://www.ms.t.kanazawa-u.ac.jp/~maths/kanjin/kanjpaper.htm

    • Related Report
      2011 Final Research Report
  • [Remarks]

    • URL

      http://www.ms.t.kanazawa-u.ac.jp/~maths/kanjin/kanjpaper.htm

    • Related Report
      2011 Annual Research Report
  • [Remarks]

    • URL

      http://kurt.kanazawa-u.ac.jp/souran_ku/info.php?teacher_id=411

    • Related Report
      2011 Annual Research Report
  • [Remarks]

    • URL

      http://www.ms.t.kanazawa-u.ac.jp/~maths/kanjin/kanjpaper.htm

    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://kurt.kanazawa-u.ac.jp/souran_ku/info.php?teacher_id=411

    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://www.ms.t.kanazawa-u.ac.jp/~maths/kanjin/kanjpaper.htm

    • Related Report
      2009 Annual Research Report

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Published: 2009-04-01   Modified: 2016-04-21  

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