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Potential analysis of various function spaces and application

Research Project

Project/Area Number 22540192
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionHiroshima Institute of Technology (2011-2013)
Hiroshima University (2010)

Principal Investigator

MIZUTA Yoshihiro  広島工業大学, 工学部, 教授 (00093815)

Co-Investigator(Kenkyū-buntansha) 大野 貴雄  大分大学 (40508511)
Project Period (FY) 2010-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywordsポテンシャル解析 / 関数空間 / 偏微分方程式 / ソボレフの定理 / 変動指数 / 極大関数 / Morrey 空間 / 調和関数 / 複素解析
Research Abstract

To develop various phenomena surrounding our nature by applying Mathematical method, a theory of partial differential equation is a crucial mathematical tool. To do so, our first task is to find a suitable partial differential equation describing a phenomenon and analyze a solution of the equation, and then we can predict our near future. For this purpose, function spaces play an important role.
In our study, we extend the famous theory developed by Sobolev and investigate tremendous phenomena as applications. It will be expected to give further development of our theory for human welfare.

Report

(5 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (18 results)

All 2014 2013 2012 2011 2010

All Journal Article (17 results) (of which Peer Reviewed: 7 results) Presentation (1 results)

  • [Journal Article] Sobolev's theorem and duality for Herz-Morrey spaces of variable exponent2014

    • Author(s)
      Yoshihiro Mizuta and Takao Ohno
    • Journal Title

      Ann. Acad. Sci. Fenn. Math.

      Volume: 39 Pages: 389-416

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Journal Article] Littlewood-Paley theory for variable exponent Lebesgue spaces and Gagliardo-Nirenberg inequality for Riesz potentials2013

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

      J. Math. Soc. Japan

      Volume: 65 Pages: 633-670

    • NAID

      10031177293

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Journal Article] Trudinger's inequality and continuity of potentials on Musielak-Orlicz-Morrey spaces2013

    • Author(s)
      Fumi-Yuki Maeda, Yoshihiro Mizuta, Takao Ohno and Tetsu Shimomura
    • Journal Title

      Potential Anal.

      Volume: 38 Pages: 515-535

    • Related Report
      2013 Final Research Report
  • [Journal Article] Boundedness of maximal operators and Sobolev's inequality on Musielak-Orlicz-Morrey spaces2013

    • Author(s)
      Fumi-Yuki Maeda, Yoshihiro Mizuta, Takao Ohno and Tetsu Shimomura
    • Journal Title

      Bull. Sci. math.

      Volume: 37 Pages: 76-96

    • Related Report
      2013 Final Research Report
  • [Journal Article] Hardy averaging operator on generalized Banach function spaces and duality2013

    • Author(s)
      Yoshihiro Mizuta, Ales Nekvinda and Tetsu Shimomura
    • Journal Title

      Z. Anal. Anwend.

      Volume: 32 Pages: 233-255

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Journal Article] Mean continuity for potentials of functions in Musielak-Orlicz spaces2013

    • Author(s)
      Fumi-Yuki Maeda, Yoshihiro Mizuta, Takao Ohno and Tetsu Shimomura
    • Journal Title

      RIMSKokyuroku Bessatsu

      Volume: B43 Pages: 67-86

    • Related Report
      2013 Final Research Report
  • [Journal Article] Sobolev's inequality for Riesz potentials in central Lorentz-Morrey spaces of variable exponent2013

    • Author(s)
      Yoshihiro Mizuta and Takao Ohno
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B43 Pages: 101-120

    • Related Report
      2013 Final Research Report
  • [Journal Article] Maximal functions, Riesz potentials and Sobolev embeddings on Morrey-Musielak-Orlicz spaces of variable exponent in R^n2012

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

      Rev. Mat. Complut.

      Volume: 25 Pages: 413-434

    • Related Report
      2013 Final Research Report
  • [Journal Article] Gagliardo-Nirenberg inequality for generalized Riesz potentials of functions in Musielak-Orlicz spaces2012

    • Author(s)
      Yoshihiro Mizuta, Eiichi Nakai, Yoshihiro Sawano, Tetsu Shimomura
    • Journal Title

      Archiv der Mathematik

      Volume: 98 Issue: 3 Pages: 253-263

    • DOI

      10.1007/s00013-012-0362-6

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Maximal functions, Riesz potentials and Sobolev embeddings on Musielak-Orlicz-Morrey spaces of variable exponent in R^n2012

    • Author(s)
      Yoshihiro Mizuta
    • Journal Title

      Rev. Mat. Complut.

      Volume: 25 Issue: 2 Pages: 413-434

    • DOI

      10.1007/s13163-011-0074-7

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Orlicz-Sobolev capacity of balls2011

    • Author(s)
      Toshihide Futamura, Yoshihiro Mizuta, Takao Ohno and Tetsu Shimomura
    • Journal Title

      Illinois Math. J.

      Volume: 55 Pages: 543-553

    • Related Report
      2013 Final Research Report
  • [Journal Article] Capacity for potentials of functions in Musielak-Orlicz spaces2011

    • Author(s)
      F.-Y.Maeda, Y.Mizuta, T.Ohno, T.Shimomura
    • Journal Title

      Nonlinear Anal.

      Volume: 74 Issue: 17 Pages: 6231-6243

    • DOI

      10.1016/j.na.2011.06.003

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Riesz potentials and Sobolev embeddings on Morrey spaces of variable exponent2011

    • Author(s)
      Y.Mizuta, E.Nakai, T.Ohno, T.Shimomura
    • Journal Title

      Complex Var.Elliptic Equ.

      Volume: 56 Issue: 7-9 Pages: 671-695

    • DOI

      10.1080/17476933.2010.504837

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Weighted Orlicz-Riesz capacity of balls2010

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

      Proc. Amer. Math. Soc.

      Volume: 138 Pages: 4291-4302

    • NAID

      120002753735

    • Related Report
      2013 Final Research Report
  • [Journal Article] Approximate identities in variable Lebesgue-Orlicz spaces L^<p・>(log L)^<q(・)>2010

    • Author(s)
      Fumi-Yuki Maeda, Yoshihiro Mizuta, Takao Ohno
    • Journal Title

      Ann.Acad.Sci.Fenn.Math.

      Volume: 35 Pages: 405-420

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Weighted Orlicz-Riesz capacity of balls2010

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

      Proc.Amer.Math.Soc.

      Volume: 138 Pages: 4291-4302

    • NAID

      120002753735

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Boundedness of fractional integral operators on Morrey spacesand Sobolev embeddings for generalized Riesz potentials2010

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

      Math.Soc.Japan

      Volume: 62 Pages: 707-744

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] Maximal functions in variable exponent Lebesgue spaces2010

    • Author(s)
      水田義弘
    • Organizer
      実解析学シンポジウム
    • Place of Presentation
      九州工業大学
    • Year and Date
      2010-11-12
    • Related Report
      2010 Annual Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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