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Potential theoretical research for nonlinear partial differential equations

Research Project

Project/Area Number 20540196
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionFukuyama Heisei University (2010-2011)
Fukuyama University (2008-2009)

Principal Investigator

ONO Takayori  福山平成大学, 福祉健康学部, 准教授 (60289270)

Co-Investigator(Kenkyū-buntansha) FUTAMURA Toshihide  大同大学, 教養部, 准教授 (90387605)
SHIMOMURA Tetsu  広島大学, 教育学研究科, 准教授 (50294476)
Project Period (FY) 2008 – 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: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords非線形偏微分方程式 / ポテンシャル論 / 優調和関数 / 除去可能集合 / 変動関数指数 / 関数空間 / ソボレフの不等式 / リースポテンシャル / Hausdorff測度 / 優多重調和関数 / 函数空間 / 変動函数指数 / 重調和関数
Research Abstract

We studied nonlinear potential theory for quasilinear partial differential equations with lower order terms. We investigated properties of superharmonic functions relative to the equation. Moreover, we characterized removable sets for continuous solutions of the equation. Also, we investigated Sobolev's inequality for functions in function spaces of variable exponent, super-polyharmonic functions and superbiharmonic functions, and boundary behavior of monotone functions in function spaces with variable exponent.

Report

(6 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report   Self-evaluation Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (64 results)

All 2011 2010 2009 2008 Other

All Journal Article (40 results) (of which Peer Reviewed: 35 results) Presentation (24 results)

  • [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 2011 Final 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 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Iterated maximal functions in variable exponent Lebesgue spaces2011

    • Author(s)
      P.Harjulehto, P.Hasto, Y.Mizuta, T.Shimomura
    • Journal Title

      Manuscripta Math.

      Volume: 135 Issue: 3-4 Pages: 381-399

    • DOI

      10.1007/s00229-010-0421-x

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] A Montel type result for super-polyharmonic functions on R^k2011

    • Author(s)
      T. Futamura, K. Kitaura, Y. Mizuta
    • Journal Title

      Potential Anal.

      Volume: Vol.34 Issue: 1 Pages: 89-100

    • DOI

      10.1007/s11118-010-9183-z

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Weighted Orlicz-Riesz capacity of balls,Proc2010

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

      Amer. Math. Soc

      Volume: 138 Issue: 12 Pages: 4291-4302

    • DOI

      10.1090/s0002-9939-2010-10510-5

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Sobolev's inequality for Riesz potentials of functions in Morrey spaces of integral form2010

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

      Math. Nachr

      Volume: 283No.9 Issue: 9 Pages: 1336-1352

    • DOI

      10.1002/mana.200710122

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Boundedness of fractional integral operators on Morrey spaces and Sobolev embeddings for generalized Riesz potentials2010

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

      Journal of the Mathematical Society of Japan

      Volume: 62 Issue: 3 Pages: 707-744

    • DOI

      10.2969/jmsj/06230707

    • NAID

      10027870763

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Sobolev inequalities for Orlicz spaces of two variable exponents2010

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

      Glasgow Math. J

      Volume: 52 Issue: 2 Pages: 227-240

    • DOI

      10.1017/s0017089509990292

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Integrability of maximal functions and Riesz potentials in Orlicz spaces of variable exponent2010

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

      J. Math. Anal. Appl

      Volume: 366No.2 Issue: 2 Pages: 391-417

    • DOI

      10.1016/j.jmaa.2010.01.053

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Compact embeddings for Sobolev spaces of variable exponents and existence of solutions for nonlinear elliptic problems involving the$ p(x)$ Laplacian and its critical exponent2010

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

      Ann. Acad. Sci. Fenn. Math

      Volume: 35 Pages: 115-130

    • DOI

      10.5186/aasfm.2010.3507

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Continuity properties for Riesz potentials of functions in Morrey spaces of variable exponent2010

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

      Math. Inequal. Appl

      Volume: 13 Issue: 1 Pages: 99-122

    • DOI

      10.7153/mia-13-08

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Sobolev embeddings for Riesz potential spaces of variable exponents near$ 1$ and Sobolev's exponent2010

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

      Bull. Sci. Math

      Volume: 134 Issue: 1 Pages: 12-36

    • DOI

      10.1016/j.bulsci.2009.09.004

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Integrability of maximal functions and Riesz potentials in Orlicz spaces of variable exponent2010

    • Author(s)
      Futamura, Toshihide; Mizuta, Yoshihiro; Shimomura, Tetsu
    • Journal Title

      Journal of Mathematical Analysis and Applications

    • Related Report
      2010 Annual Research Report 2010 Self-evaluation Report
  • [Journal Article] Sobolev inequalities for Orlicz spaces of two variable exponents2010

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

      Glasgow Mathematical Journal

      Volume: 52 Pages: 227-240

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Compact embeddings for Sobolev spaces of variable exponents and existence of solutions for nonlinear elliptic problems involving the $p(x)$-Laplacian and its critical exponent2010

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

      Annales Academiae Scientiarum Fennicae

      Volume: 35 Pages: 115-130

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Maximal functions in variable exponent spaces : limiting cases of the exponent2009

    • Author(s)
      L. Diening, P. Harjulehto, P. Hasto, Y. Mizuta and T. Shimomura
    • Journal Title

      Ann. Acad. Sci. Fenn. Math

      Volume: 34 Pages: 503-522

    • URL

      http://www.acadsci.fi/mathematica/Vol34/DieningHarjulehtoHastoMizutaShimomura.html

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] CONTINUITY PROPERTIES OF RIESZ POTENTIALS OF ORLICZ FUNCTIONS2009

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

      Tohoku Mathematical Journal, Second Series

      Volume: 61 Issue: 2 Pages: 225-240

    • DOI

      10.2748/tmj/1245849445

    • NAID

      130003339584

    • ISSN
      0040-8735, 2186-585X
    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Riesz decomposition for superbiharmonic functions in the unit ball2009

    • Author(s)
      T. Futamura, K. Kitaura, Y. Mizuta
    • Journal Title

      Hookaido Math. J

      Volume: Vol.38 Pages: 683-700

    • URL

      http://hmj2.math.sci.hokudai.ac.jp/1334/

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On solutions of quasilinear elliptic equations with general structure2009

    • Author(s)
      T.Ono
    • Journal Title

      RIMS 研究集会報告集 1669

      Pages: 144-147

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Continuity properties of Riesz potentials of Orlicz functions2009

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

      Tohoku Math.J. 61

      Pages: 225-240

    • NAID

      110007129528

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Sobolev's inequality for Riesz potentials of functions in non-doubling Morrey spaces2009

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

      Osaka J.Math. 46

      Pages: 255-271

    • NAID

      120005986679

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Maximal functions in variable exponent spaces : limiting cases of the exponent2009

    • Author(s)
      L.Diening, P.Harjulehto, P.Hasto, Y.Mizuta, T.Shimomura
    • Journal Title

      Ann.Acad.Sci.Fenn.Math. 34

      Pages: 503-522

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Integrability of maximal functions for generalized Lebesgue spaces $L^{p(\cdot)}(\logL)^{q(\cdot)}$2009

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

      Proceedings of the Conference on Potential Theory and Stochastics in Albac Aurel Cornea Memorial Volume

      Pages: 193-202

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Variable exponent spaces on metric measure spaces2009

    • Author(s)
      T.Futamura, P.Harjulehto, P.Hasto, Y.Mizuta, T.Shimomura
    • Journal Title

      World Scientific

      Pages: 107-121

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Variable exponent spaces on metric measure spaces2009

    • Author(s)
      Toshihide Futamura, Keiji Kitaura, Yoshihiro Mizuta
    • Journal Title

      Hokkaido Math.J. 38

      Pages: 683-700

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Integrability of maximal functions and Riesz potentials in Orlicz spaces of variable exponent2009

    • Author(s)
      Toshihide Futamura, Keiji Kitaura, Yoshihiro Mizuta
    • Journal Title

      J.Math.Anal.Appl. 366

      Pages: 391-417

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Integrability of maximal functions for generalized Lebesgue spaces with variable exponent2008

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

      Math. Nachr

      Volume: No.3 Issue: 3 Pages: 386-395

    • DOI

      10.1002/mana.200510609

    • Related Report
      2011 Final Research Report
  • [Journal Article] Sobolev embeddings for Riesz potentials of functions in Morrey spaces of variable exponent2008

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

      J. Math. Soc. Japan

      Volume: No.2 Pages: 583-602

    • NAID

      10024331805

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Isolated singularities, growth of spherical means and Riesz decomposition for superbiharmonic functions2008

    • Author(s)
      T. Futamura, K. Kitaura, Y. Mizuta
    • Journal Title

      Hiroshima Math. J

      Volume: Vol.38 Pages: 231-241

    • NAID

      110006794234

    • URL

      http://projecteuclid.org/euclid.hmj/1220619459

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Superharmonic functions and differential equations involving measures for quasilinear elliptic operators with lower order terms2008

    • Author(s)
      T. Ono
    • Journal Title

      Ann. Acad. Sci. Fenn. Math

      Volume: 33 Pages: 171-204

    • URL

      http://www.acadsci.fi/mathematica/Vol33/vol33pp171-204.pdf

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Superharmonic functions and differential equations involving measures for quasilinear elliptic operators with lower order terms2008

    • Author(s)
      T.Ono
    • Journal Title

      Ann.Acad.Sci.Fenn..Math.

    • Related Report
      2010 Self-evaluation Report
  • [Journal Article] Lindelof theorems for monotone Sobolev functions with variable exponent2008

    • Author(s)
      T.Futamura, T.Shimomura
    • Journal Title

      Proc.Japan Acad.Ser.A Math.Sci

    • NAID

      40015882843

    • Related Report
      2010 Self-evaluation Report
  • [Journal Article] Superharmonic functions and differential equations involving measures for quasilinear elliptic operators with lower order terms2008

    • Author(s)
      T. Ono
    • Journal Title

      Ann. Acad. Sci. Fenn. Math. 33

      Pages: 171-204

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Isolated singularites, growth of spherical means and Rieszdecomposition for superbiharmonic functions2008

    • Author(s)
      T. Futamura, K. Kitaura, Y. Mizuta
    • Journal Title

      Hiroshima Math. J. 38

      Pages: 231-241

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Integrability of maximal functions for generalized Lebesgue spaces with variable exponent2008

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

      Math. Nachr 281

      Pages: 386-395

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Lindel\" of theorems for monotone Sobolev functions with variable exponent2008

    • Author(s)
      T. Futamura, T. Shimomura
    • Journal Title

      Proc. Japan Acad. Ser. A Math. Sci. 84

      Pages: 25-28

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Sobolev embeddings for Riesz potentials of functions in Morrey spaces of variable exponent2008

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

      J. Math. Soc. Japan 60

      Pages: 583-602

    • NAID

      10024331805

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Sobolev's inequalities and vanishing integrability for Riesz potentials of fundions in the generalized Lebesgue space $L^{p(\cdot)} (\log L)^{q(\cdot)}$2008

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

      J. Math. Anal. Appl. 345

      Pages: 70-85

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An elementary proof of Sobolev embeddings for Riesz potentials of fundions in Morrey spaces $L^{1,\nu,\beta} (G)$2008

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

      Hiroshima Math. J. 38

      Pages: 425-436

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Removable sets for H\"{o} lder continuous solutions of quasilinear elliptic equations with lower order terms

    • Author(s)
      T. Ono
    • Journal Title

      Math. Ann

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Presentation] 重み付き準線形楕円型方程式の解のヘルダー連続性について2011

    • Author(s)
      小野太幹
    • Place of Presentation
      岐阜大学
    • Year and Date
      2011-11-05
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Presentation] Exponential integrability of Riesz potentials of Orlicz functions2011

    • Author(s)
      下村哲
    • Organizer
      ポテンシャル論研究集会
    • Place of Presentation
      岐阜大学
    • Year and Date
      2011-11-05
    • Related Report
      2011 Final Research Report
  • [Presentation] Iterated maximal functions in variable exponent Lebesgue spaces2011

    • Author(s)
      下村哲
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      信州大学
    • Year and Date
      2011-09-30
    • Related Report
      2011 Final Research Report
  • [Presentation] Weighted Sobolev inequality in Musielak-Orlicz space2010

    • Author(s)
      下村哲
    • Organizer
      ポテンシャル論研究集会
    • Place of Presentation
      大分大学
    • Year and Date
      2010-11-05
    • Related Report
      2011 Final Research Report
  • [Presentation] Hardy's inequality in Orlicz-Sobolev spaces of variable exponent2010

    • Author(s)
      水田義弘、中井英一、大野貴雄、下村哲
    • Organizer
      日本数学会2010年度秋季総合分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-22
    • Related Report
      2010 Annual Research Report
  • [Presentation] Sobolev inequalities for variable exponent Orlicz spaces2010

    • Author(s)
      下村哲
    • Organizer
      第49回実函数論・函数解析学合同シンポジウム
    • Place of Presentation
      東京理科大学
    • Year and Date
      2010-08-02
    • Related Report
      2011 Final Research Report
  • [Presentation] Orlicz-Sobolev capacity of balls2010

    • Author(s)
      下村哲
    • Organizer
      日本数学会春季総合分科会
    • Place of Presentation
      慶応大学
    • Year and Date
      2010-03-24
    • Related Report
      2011 Final Research Report
  • [Presentation] Sobolev inequalities in variable exponent Orlicz spaces2009

    • Author(s)
      Tetsu Shimomura
    • Organizer
      International Workshop on Potential Theory in Hokkaido 2009
    • Place of Presentation
      Hokkaido University, Department of Mathematics
    • Year and Date
      2009-11-02
    • Related Report
      2011 Final Research Report
  • [Presentation] Maximal functions in variable exponent spaces : limiting cases of the exponent2009

    • Author(s)
      下村哲
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-27
    • Related Report
      2011 Final Research Report
  • [Presentation] SMaximal functions in variable exponent spaces : limiting cases of the exponent2009

    • Author(s)
      T.Shimomura
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-27
    • Related Report
      2009 Annual Research Report
  • [Presentation] Removable sets for continuous solutions of quasilinear elliptic equations with lower order terms2009

    • Author(s)
      Takayori ONO
    • Organizer
      International Workshop on Potential Theory 2009
    • Place of Presentation
      Hokkaido University, Department of Mathematics
    • Year and Date
      2009-09-02
    • Related Report
      2011 Final Research Report
  • [Presentation] Sobolev inequalities in variable exponent Orlicz spaces2009

    • Author(s)
      T.Shimomura
    • Organizer
      International Workshop on Potential Theory in Hokkaido 2009
    • Place of Presentation
      Hokkaido University
    • Year and Date
      2009-09-02
    • Related Report
      2009 Annual Research Report
  • [Presentation] Removable sets for continuous solutions of quasilinear elliptic equations with lower order terms2009

    • Author(s)
      T.Ono
    • Organizer
      International Workshop on Potential Theory in Hokkaido 2009
    • Place of Presentation
      Hokkaido University
    • Year and Date
      2009-09-01
    • Related Report
      2009 Annual Research Report
  • [Presentation] 変動指数をもつ関数空間におけるリースポテンシャルのハーディー型不等式2009

    • Author(s)
      二村俊英
    • Organizer
      日本数学会年会
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-28
    • Related Report
      2011 Final Research Report
  • [Presentation] 変動指数をもつ関数空間におけるリースポテンシャルのハーディー型不等式2009

    • Author(s)
      二村俊英
    • Organizer
      日本数学会春季総合分科会
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-28
    • Related Report
      2008 Annual Research Report
  • [Presentation] On solutions of quasilinear elliptic equations with general structure2009

    • Author(s)
      小野太幹
    • Organizer
      ポテンシャル論とその関連分野研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-02-17
    • Related Report
      2011 Final Research Report
  • [Presentation] Integrability of maximal functions and Riesz potentials in Orlicz spaces of variable exponent2009

    • Author(s)
      下村哲
    • Organizer
      ポテンシャル論とその関連分野研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-02-17
    • Related Report
      2011 Final Research Report 2008 Annual Research Report
  • [Presentation] On solutions of quasilinear elliptic equations with general structure2009

    • Author(s)
      小野太幹
    • Organizer
      ポテンシャル論とその関連分野
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-02-16
    • Related Report
      2008 Annual Research Report
  • [Presentation] Removable sets for continuous solutions of quasilinear elliptic equations with lower order terms2009

    • Author(s)
      T.Ono
    • Organizer
      International Workshop on Potential Theory
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Continuity properties for Riesz potentials of functions in Morrey spaces of variable exponent2008

    • Author(s)
      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
      2008-09-26
    • Related Report
      2011 Final Research Report 2008 Annual Research Report
  • [Presentation] Sobolev's inequalities for Riesz potentials of functions in the generalized Lebesgue space2008

    • Author(s)
      Tetsu Shimomura
    • Organizer
      FSDONA Workshop
    • Place of Presentation
      Helsinki University, Finland
    • Year and Date
      2008-08-22
    • Related Report
      2011 Final Research Report
  • [Presentation] Sobolev's inequalities for Riesz potentials of functions in the generalized Lebesgue space$L^{p(\cdot)}(\log L)^{q(\cdot)}$2008

    • Author(s)
      Tetu Shimomura
    • Organizer
      FSDONA Workshop
    • Place of Presentation
      Finland. Helsinki University
    • Year and Date
      2008-08-22
    • Related Report
      2008 Annual Research Report
  • [Presentation] 変動指数をもつ関数空間におけるリースポテンシャルのハーディー型不等式

    • Author(s)
      二村俊英、水田義弘、下村哲
    • Organizer
      日本数学会2009年度年会
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Hardy's inequality in Orlicz-Sobolev spaces of variable exponent

    • Author(s)
      水田義弘、中井英一、大野貴雄、下村哲
    • Organizer
      日本数学会2010年度秋季総合分科会
    • Related Report
      2010 Self-evaluation Report

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Published: 2008-04-01   Modified: 2016-04-21  

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