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Potential analysis for Bergman spaces

Research Project

Project/Area Number 18540169
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionMeijo University (2008-2009)
Nagoya University (2006-2007)

Principal Investigator

SUZUKI Noriaki  Meijo University, 理工学部, 教授 (50154563)

Co-Investigator(Kenkyū-buntansha) 西尾 昌治  大阪市立大学, 理学研究科, 准教授 (90228156)
下村 勝孝  茨城大学, 理学部, 准教授 (00201559)
山田 雅博  岐阜大学, 教育学部, 准教授 (00263666)
Co-Investigator(Renkei-kenkyūsha) NISHIO Masaharu  大阪市立大学, 大学院・理学研究科, 准教授 (90228156)
SHIMOMURA Katsunori  茨城大学, 理学部, 准教授 (00201559)
YAMADA Masahiro  岐阜大学, 教育学部, 准教授 (00263666)
Project Period (FY) 2006 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥4,050,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥750,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2006: ¥800,000 (Direct Cost: ¥800,000)
Keywords放物型作用素 / Bergman空間 / Carleson埋め込み / Toeplitz作用素 / ポテンシャル論 / ベルグマン空間 / 関数解析学 / ポテンシャル解析 / Carleson測度 / テープリッツ作用素
Research Abstract

Unifying the Laplace and the heat operators, we introduce parabolic operators on the upper half space and define parabolic Bergman spaces. We study some linear operators acting on them, in particular, we show the boundedness and compactness of Carleson imbedding and Toeplitz operators.

Report

(6 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report   Self-evaluation Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (32 results)

All 2010 2009 2008 2007 2006

All Journal Article (24 results) (of which Peer Reviewed: 14 results) Presentation (8 results)

  • [Journal Article] Carleson inequalities on parabolic Bergman spaces2010

    • Author(s)
      M. Nishio, N. Suzuki, M. Yamada
    • Journal Title

      Tohoku Math. J. 62(to appear)

    • NAID

      110007608300

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] 放物型ベルグマン空間上の作用素について2010

    • Author(s)
      M. Nishio, N. Suzuki, M. Yamada
    • Journal Title

      京都大学数理解析研究所講究録 (掲載予定)

    • Related Report
      2009 Final Research Report
  • [Journal Article] Weighted Berezin transformations with application to Toeplitz operators of Schatten class on parabolic Bergman spaces2009

    • Author(s)
      M. Nishio, N. Suzuki, M. Yamada
    • Journal Title

      Kodai Math. J. 32

      Pages: 501-520

    • NAID

      130004687919

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Potential analysis of parabolic Bergman spaces2009

    • Author(s)
      N. Suzuki
    • Journal Title

      Research reports of Faculty of Sci. and Tech. Meijo University 49

      Pages: 5-12

    • NAID

      40019824347

    • Related Report
      2009 Final Research Report
  • [Journal Article] Toeplitz operators of Schatten class on the parabolic Bergman space2009

    • Author(s)
      M. Nishio, N. Suzuki, M. Yamada
    • Journal Title

      Procedding of 16^<th> ICFIDCAA

      Pages: 305-311

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Potential Analysis of parabolic Bergman sapces2009

    • Author(s)
      N.Suzuki
    • Journal Title

      Research Repots of Fac.Of Sci.and Tecj.Meijo Univ. 49

      Pages: 5-12

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Weighted Berezin transformations with application to Toeplitz operators of Schatten class on Parabolic Bergman spaces2009

    • Author(s)
      N.Nishio
    • Journal Title

      Kodai Math J. 32

      Pages: 501-520

    • NAID

      130004687919

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Toeplitz operators of Schatten class on the parabolic Bergman space2009

    • Author(s)
      N.Nishio
    • Journal Title

      Proceedings of 16^<th> ICFIDCAA 1

      Pages: 305-311

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Compact Toeplitz operators on parabolic Bergman spaces2008

    • Author(s)
      M. Nishio, N. Suzuki, M. Yamada
    • Journal Title

      Hiroshima Math. J. 38

      Pages: 177-192

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Interpolating sequences of parabolic Bergman spaces2008

    • Author(s)
      M. Nishio, N. Suzuki, M. Yamada
    • Journal Title

      Potential analysis 28

      Pages: 357-378

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Parabolic dilations with application to Toeplitz operators on parabolic Bergman sapaces2008

    • Author(s)
      M. Nishio, N. Suzuki, M. Yamada
    • Journal Title

      Proceedings of 15^<th> ICFIDCAA, OMUP

      Pages: 307-312

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Compact Toeplitz operators on parabolic Bergman spaces2008

    • Author(s)
      M.Nishio, N.Suzuki, and M.Yamada
    • Journal Title

      Hiroshima Math J.38

      Pages: 177-192

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] Interpolating sequences of parabolic Bergman spaces2008

    • Author(s)
      M.Nishio, N.Suzuki, and M.Yamada
    • Journal Title

      Potential analysis 28

      Pages: 357-378

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] Parabplic dilations with application to Toeplitz operators on parabolic Bergmansapaces2008

    • Author(s)
      M.Nishio, N.Suzuki, and M.Yamada
    • Journal Title

      Proceedings of 15th ICFIDCAA,OMUP

      Pages: 307-312

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] Parabolic dilations with application to Toeplitz operators on parabolic Berqman spaces2008

    • Author(s)
      M. Nishio
    • Journal Title

      Proceedings of 15^<th> ICFIDCAA, OMUP 2

      Pages: 307-312

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Compact Toeplitz operators on parabolic Bergman spaces2008

    • Author(s)
      M. Nisho
    • Journal Title

      Hiroshima Math. J. 38

      Pages: 177-192

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Interpolating sequences of parabolic Bergman spaces2008

    • Author(s)
      M. Nisho
    • Journal Title

      Potential Analysis 28

      Pages: 357-378

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Toeplitz operators and Carleson measures on parabolic Bergman spaces2007

    • Author(s)
      M. Nishio, N. Suzuki, M. Yamada
    • Journal Title

      Hokkaido Math. J. 36

      Pages: 363-583

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] 放物型Bergman空間上のToeplitz作用素2007

    • Author(s)
      M. Nishio, N. Suzuki, M. Yamada
    • Journal Title

      京都大学数理解析研究所講究録 1553

      Pages: 181-195

    • Related Report
      2009 Final Research Report
  • [Journal Article] Toeplitz operators and Carleson measureson parabolic Bergman spaces2007

    • Author(s)
      M.Nishio, N.Suzuki, and M.Yamada
    • Journal Title

      Hokkaido Math J.36

      Pages: 363-583

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] Toeplitz operatons and Carleson measunes on parabehic Bergman spaces2007

    • Author(s)
      M. Nishio
    • Journal Title

      Hokkaido Math. J. 36

      Pages: 563-583

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Lp boundedness of Bergman projections forα-parabplic operators2006

    • Author(s)
      M. Nishio, K. Shimomura, N. Suzuki
    • Journal Title

      ASPM 44

      Pages: 305-318

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Lp boundedness of Bergman projections for α-parabplic operators2006

    • Author(s)
      M.Nishio, K.Shimomura, and N.Suzuki
    • Journal Title

      ASPM 44

      Pages: 305-318

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] L^P-loundedneas of Bingman projection for α-panaldic openators2006

    • Author(s)
      M.Nishio
    • Journal Title

      Advanced Studies in Pwv Mathematics 44

      Pages: 305-318

    • Related Report
      2006 Annual Research Report
  • [Presentation] 放物型Bergman空間上のSchatten-Herz族Toeplitz作用素について2010

    • Author(s)
      西尾昌治
    • Organizer
      日本数学会2010年度年会
    • Place of Presentation
      慶応義塾大学(横浜)
    • Year and Date
      2010-03-24
    • Related Report
      2009 Final Research Report
  • [Presentation] 放物型 Bergman 空間上の Schatten-Herz 族 Toeplitz 作用素について2010

    • Author(s)
      西尾昌治
    • Organizer
      日本数学会2010年度年会
    • Place of Presentation
      慶応大学理工学部(横浜)
    • Year and Date
      2010-03-24
    • Related Report
      2009 Annual Research Report
  • [Presentation] 放物型Bergman空間における指数1以下のSchatten族Toeplitz作用素の特徴付け2009

    • Author(s)
      西尾昌治
    • Organizer
      日本数学会2009年度年会
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-28
    • Related Report
      2009 Final Research Report
  • [Presentation] Toeplitz operators of Schatten class on the parabolic Bergman spaces2008

    • Author(s)
      西尾昌治
    • Organizer
      日本数学会2008年秋季総合分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-24
    • Related Report
      2009 Final Research Report
  • [Presentation] Carleson inequalities on parabolic Bergman spaces2008

    • Author(s)
      西尾昌治
    • Organizer
      日本数学会2008年度年会
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-24
    • Related Report
      2009 Final Research Report
  • [Presentation] Interpolating sequences of parabolic Bergman spaces2007

    • Author(s)
      山田雅博
    • Organizer
      日本数学会2007年秋季総合分科会
    • Place of Presentation
      埼玉大学
    • Year and Date
      2007-03-30
    • Related Report
      2009 Final Research Report
  • [Presentation] 放物型Bergman空間におけるToeplitz作用素のコンパクト性2006

    • Author(s)
      西尾昌治
    • Organizer
      日本数学会2006年秋季総合分科会
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2006-09-19
    • Related Report
      2009 Final Research Report
  • [Presentation] On parabolic Bergman spaces2006

    • Author(s)
      N. Suzuki
    • Organizer
      International Congress of Mathematics
    • Place of Presentation
      Madrid (Spain) (poster)
    • Year and Date
      2006-08-24
    • Related Report
      2009 Final Research Report

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Published: 2006-04-01   Modified: 2016-04-21  

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