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A new trend of function spaces with variable exponents

Research Project

Project/Area Number 26400154
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionHiroshima University (2016-2017)
Hiroshima Institute of Technology (2014-2015)

Principal Investigator

Mizuta Yoshihiro  広島大学, 理学研究科, 名誉教授 (00093815)

Co-Investigator(Kenkyū-buntansha) 山内 雄介  広島工業大学, 工学部, 准教授 (00451435)
大野 貴雄  大分大学, 教育学部, 准教授 (40508511)
小山 哲也  広島工業大学, 工学部, 教授 (50170402)
Project Period (FY) 2014-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywordsfunction space / variable exponent / Sovolev theorem / ポテンシャル論 / 関数空間 / ソボレフの不等式 / 変動指数をもつ関数空間 / 偏微分方程式 / ソボレフの定理 / 変動指数 / ポテンシャル
Outline of Final Research Achievements

To develop various phenomena surrounding our nature by applying Mathematical method, a theory of partial differential equation is used. To do so, our first task is to find partial differential equation describing phenomena and analyze solution of the equation. For this purpose, function spaces play an important role.
In our study, we extend the theory developed by Sobolev, which will be used to investigates various phenomena. It will be expected to give further development of our theory.

Report

(5 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (6 results)

All 2017 2016 2015 2014

All Journal Article (5 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 5 results,  Open Access: 3 results) Presentation (1 results) (of which Invited: 1 results)

  • [Journal Article] Growth properties for Riesz potentials of functions in weighted variable L^p(・) spaces2017

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

      Nonlinear Analysis

      Volume: 162 Pages: 49-75

    • DOI

      10.1016/j.na.2017.06.010

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Growth properties near the origin for generalized Riesz potentials2017

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

      J. Math. Anal. Appl.

      Volume: 54 Issue: 1 Pages: 285-302

    • DOI

      10.1016/j.jmaa.2017.04.068

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Duality of Herz-Morrey Spaces of Variable Exponent2016

    • Author(s)
      Yoshihiro Mizuta
    • Journal Title

      Filomat

      Volume: 30 Issue: 7 Pages: 1891-1898

    • DOI

      10.2298/fil1607891m

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Boundedness of the maximal operator and Sobolev's inequality on non-homogeneous central Herz-Morrey-Orlicz spaces2015

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

      Nonlinear Anal.

      Volume: 128 Pages: 325-347

    • DOI

      10.1016/j.na.2015.08.014

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] SOBOLEV’S THEOREM AND DUALITY FOR HERZ-MORREY SPACES OF VARIABLE EXPONENT2014

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

      Ann. Acad. Sci. Fenn. Math.

      Volume: 39 Pages: 389-416

    • DOI

      10.5186/aasfm.2014.3913

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] 変動指数をもつ関数空間2017

    • Author(s)
      水田義弘
    • Organizer
      日本数学会 年会
    • Place of Presentation
      首都大学東京
    • Related Report
      2016 Research-status Report
    • Invited

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Published: 2014-04-04   Modified: 2019-03-29  

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