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Harmonic analysis based on function spaces with variable exponent and its applications

Research Project

Project/Area Number 24540159
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionIbaraki University

Principal Investigator

NAKAI Eiichi  茨城大学, 理学部, 教授 (60259900)

Co-Investigator(Kenkyū-buntansha) HORIUCHI Toshio  茨城大学, 理学部, 教授 (80157057)
SOBUKAWA Takuya  早稲田大学, グローバルエデュケーションセンター, 教授 (60252946)
SADASUE Gaku  大阪教育大学, 教育学部, 准教授 (40324884)
SAWANO Yoshihiro  首都大学東京, 理工学研究科, 准教授 (40532635)
Co-Investigator(Renkei-kenkyūsha) MIZUTA Yoshihiro  広島工業大学, 工学部, 教授 (00093815)
Project Period (FY) 2012-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2012: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Keywords調和解析学 / 実解析学 / 関数空間 / 変動指数 / 分数べき積分 / 特異積分 / 調和解析 / Hardy空間 / Orlicz空間 / Campanato空間 / Morrey空間
Outline of Final Research Achievements

We established the theory of Hardy spaces with variable exponent and Orlicz-Hardy spaces, characterizing by Poisson integral, atomic decomposition, Littlewood-Paley decomposition, etc, proving the boundedness of singular and fractional integral operators, and studying related function spaces and their duals. Moreover, we developed the theory of generalized Morrey-Campanato spaces, B_sigma-Morrey-Campanato spaces, and their unified spaces as function spaces with variable oscillation and variable growth conditions. Using these function spaces, we analyzed the properties of solutions of some partial differential equations. Furthermore, we constructed the harmonic analysis theory for martingales.

Report

(4 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (53 results)

All 2015 2014 2013 2012 Other

All Journal Article (22 results) (of which Peer Reviewed: 22 results,  Acknowledgement Compliant: 4 results,  Open Access: 3 results) Presentation (28 results) (of which Invited: 14 results) Remarks (3 results)

  • [Journal Article] Pointwise multipliers on martingale Campanato spaces2014

    • Author(s)
      Eiichi Nakai and Gaku Sadasue
    • Journal Title

      Studia Mathematica

      Volume: 220 Issue: 1 Pages: 87-100

    • DOI

      10.4064/sm220-1-5

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Characterizations for the generalized fractional integral operators on Morrey spaces2014

    • Author(s)
      Eridani, Hendra Gunawan, Eiichi Nakai, and Yoshihiro Sawano
    • Journal Title

      Math. Inequal. Appl.

      Volume: 17 Issue: 2 Pages: 761-777

    • DOI

      10.7153/mia-17-56

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Orlicz-Hardy spaces and their duals2014

    • Author(s)
      Eiichi Nakai and Yoshihiro Sawano
    • Journal Title

      Science China Mathematics

      Volume: 57 Issue: 5 Pages: 903-962

    • DOI

      10.1007/s11425-014-4798-y

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Weighted Hardy inequalities with infinitely many sharp missing terms2014

    • Author(s)
      Hiroshi Ando, Toshio Horiuchi and Eiichi Nakai
    • Journal Title

      Mathematical Journal of Ibaraki University

      Volume: 46

    • NAID

      130004697044

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Some properties of slowly increasing functions2014

    • Author(s)
      Hiroshi Ando, Toshio Horiuchi and Eiichi Nakai
    • Journal Title

      Mathematical Journal of Ibaraki University

      Volume: 46

    • NAID

      130004697043

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Function spaces with variable exponents -- an introduction --2014

    • Author(s)
      Mitsuo Izuki, Eiichi Nakai and Yoshihiro Sawano
    • Journal Title

      Scientiae Mathematicae Japonicae

      Volume: 77

    • NAID

      130007643061

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Boundedness of intrinsic Littlewood-Paley functions on Musielak-Orlicz Morrey and Campanato Spaces2014

    • Author(s)
      Yiyu Liang, Eiichi Nakai, Dachun Yang and Junqiang Zhang
    • Journal Title

      Banach Journal of Mathematical Analysis

      Volume: 8

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Generalized fractional integrals on generalized Morrey spaces2014

    • Author(s)
      Eiichi Nakai
    • Journal Title

      Mathematische Nachrichten

      Volume: 287 Issue: 2-3 Pages: 339-351

    • DOI

      10.1002/mana.201200334

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [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

      Journal of the Mathematical Society of Japan

      Volume: 65 Issue: 2 Pages: 633-670

    • DOI

      10.2969/jmsj/06520633

    • NAID

      10031177293

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] The Hardy-Littlewood maximal operator on Lebesgue spaces with variable exponent2013

    • Author(s)
      Mitsuo Izuki, Eiichi Nakai and Yoshihiro Sawano
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B42

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Hardy spaces with variable exponent2013

    • Author(s)
      Mitsuo Izuki, Eiichi Nakai and Yoshihiro Sawano
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B42

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Maximal function on generalized martingale Lebesgue spaces with variable exponent2013

    • Author(s)
      Eiichi Nakai and Gaku Sadasue
    • Journal Title

      Statistics & Probability Letters

      Volume: 83 Issue: 10 Pages: 2168-2171

    • DOI

      10.1016/j.spl.2013.06.007

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Martingale Morrey-Hardy and Campanato-Hardy Spaces2013

    • Author(s)
      Eiichi Nakai, Gaku Sadasue and Yoshihiro Sawano
    • Journal Title

      Journal of Function Spaces and Applications, Article ID 690258,

      Volume: 2013 Pages: 14-14

    • DOI

      10.1155/2013/690258

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Integral operators on B_{\sigma}-Morrey-Campanato spaces2013

    • Author(s)
      Yasuo Komori-Furuya, Katsuo Matsuoka, Eiichi Nakai and Yoshihiro Sawano
    • Journal Title

      Revista Matematica Complutense

      Volume: 26 Issue: 1 Pages: 1-32

    • DOI

      10.1007/s13163-011-0091-6

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Applications of Littlewood-Paley theory for $B_{\sigma}$-Morrey spaces to the boundedness of integral operators2013

    • Author(s)
      Y. Komori-Furuya, K. Matsuoka, E. Nakai and Y. Sawano
    • Journal Title

      Journal of Function Spaces and Applications., Article ID 859402

      Volume: 2013 Pages: 1-21

    • DOI

      10.1155/2013/859402

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Martingale Orlicz-Hardy spaces2012

    • Author(s)
      Takashi Miyamoto, Eiichi Nakai, Gaku Sadasue
    • Journal Title

      Mathematische Nachrichten

      Volume: 285 Issue: 5-6 Pages: 670-686

    • DOI

      10.1002/mana.201000109

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Bilinear estimates in dyadic BMO and the Navier-Stokes equations2012

    • Author(s)
      Eiichi Nakai and Tsuyoshi Yoneda
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 64 Issue: 2 Pages: 399-422

    • DOI

      10.2969/jmsj/06420399

    • NAID

      10030740240

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Hardy spaces with variable exponents and generalized Campanato spaces2012

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

      Journal of Functional Analysis

      Volume: 262 Issue: 9 Pages: 3665-3748

    • DOI

      10.1016/j.jfa.2012.01.004

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Martingale Morrey-Campanato spaces and fractional integrals2012

    • Author(s)
      Eiichi Nakai and Gaku Sadasue
    • Journal Title

      Journal of Function Spaces and Applications

      Volume: 2012 Pages: 1-29

    • DOI

      10.1155/2012/673929

    • Related Report
      2012 Research-status 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 Research-status Report
    • Peer Reviewed
  • [Journal Article] Construction of slowly increasing functions2012

    • Author(s)
      Hiroshi Ando, Toshio Horiuchi and Eiichi Nakai
    • Journal Title

      Scientiae Mathematicae Japonicae

      Volume: 75

    • NAID

      130007663411

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Generalized Stummel class and Morrey spaces2012

    • Author(s)
      Hendra Gunawan, Eiichi Nakai, Yoshihiro Sawano and Hitoshi Tanaka
    • Journal Title

      Publications de l'Institut Mathematique

      Volume: 92 Issue: 106 Pages: 127-138

    • DOI

      10.2298/pim1206127g

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] 局所 Morrey-Camapanto 空間の一般化と補間理論2015

    • Author(s)
      中井英一, 曽布川拓也
    • Organizer
      日本数学会年会
    • Place of Presentation
      明治大学駿河台キャンパス(リバティタワー)
    • Year and Date
      2015-03-21 – 2015-03-24
    • Related Report
      2014 Annual Research Report
  • [Presentation] Function spaces with variable exponent2015

    • Author(s)
      中井英一
    • Organizer
      研究集会「関数解析学の研究とその応用」
    • Place of Presentation
      新潟大学駅南キャンパス「ときめいと」
    • Year and Date
      2015-01-29 – 2015-01-30
    • Related Report
      2014 Annual Research Report
  • [Presentation] $B_w^u(E)$-関数空間の補間定理とその応用2014

    • Author(s)
      中井英一, 曽布川拓也
    • Organizer
      実解析学シンポジウム2014
    • Place of Presentation
      富山大学理学部
    • Year and Date
      2014-10-31 – 2014-11-02
    • Related Report
      2014 Annual Research Report
  • [Presentation] Wavelet characterization and modular inequalities for weighted Lebesgue spaces with variable exponent2014

    • Author(s)
      出来光夫, 中井英一, 澤野嘉宏
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      広島大学東広島キャンパス
    • Year and Date
      2014-09-25 – 2014-09-28
    • Related Report
      2014 Annual Research Report
  • [Presentation] $B_w^u$ 空間の補間定理2014

    • Author(s)
      中井英一, 曽布川拓也
    • Organizer
      関数環研究集会
    • Place of Presentation
      早稲田大学教育学部
    • Year and Date
      2014-09-18 – 2014-09-19
    • Related Report
      2014 Annual Research Report
  • [Presentation] A characterization of BLO martingales2014

    • Author(s)
      中井英一, 貞末岳
    • Organizer
      日本数学会年会
    • Place of Presentation
      学習院大学目白キャンパス
    • Related Report
      2013 Research-status Report
  • [Presentation] Lebesgue and Morrey spaces with variable exponent2013

    • Author(s)
      中井英一
    • Organizer
      月曜解析セミナー
    • Place of Presentation
      北海道大学 理学部
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Generalized fractional integrals on Morrey spaces with variable exponent2013

    • Author(s)
      Eiichi Nakai
    • Organizer
      Asian Mathematical Conference 2013
    • Place of Presentation
      Busan Exhibition and Convention Center (BEXCO), Busan, Korea
    • Related Report
      2013 Research-status Report
  • [Presentation] Pointwise multipliers on BMO and related topics2013

    • Author(s)
      Eiichi Nakai
    • Organizer
      Function spaces and their applications
    • Place of Presentation
      Beijing Normal University, Beijing, China
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Pointwise multipliers on martingale Campanato spaces2013

    • Author(s)
      貞末岳, 中井英一
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      愛媛大学城北キャンパス
    • Related Report
      2013 Research-status Report
  • [Presentation] Maximal function on generalized martingale Lebesgue spaces with variable exponent2013

    • Author(s)
      貞末岳, 中井英一
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      愛媛大学城北キャンパス
    • Related Report
      2013 Research-status Report
  • [Presentation] The Gibbs-Wilbraham, Pinsky and the third phenomena for the multiple Fourier series2013

    • Author(s)
      Shigehiko Kuratsubo and Eiichi Nakai
    • Organizer
      1st East Asian Conference in Harmonic analysis and Applications
    • Place of Presentation
      Seoul National University, Seoul, Korea
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] A note on BLO martingales2013

    • Author(s)
      中井英一, 貞末岳
    • Organizer
      実解析学シンポジウム2013
    • Place of Presentation
      岡山大学教育学部
    • Related Report
      2013 Research-status Report
  • [Presentation] Pointwise multipliers on BMO and generalized L^p spaces with variable exponent2013

    • Author(s)
      Eiichi Nakai
    • Organizer
      Seminar on harmonic analysis
    • Place of Presentation
      Xiamen University, China
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Convergence and divergence of the multiple Fourier series2013

    • Author(s)
      Eiichi Nakai
    • Organizer
      Seminar on harmonic analysis
    • Place of Presentation
      Xiamen University, China
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Generalized Morrey-Campanato spaces of martingales2013

    • Author(s)
      貞末岳, 澤野嘉宏, 中井英一
    • Organizer
      日本数学会年会
    • Place of Presentation
      京都大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Fractional integrals2012

    • Author(s)
      Eiichi Nakai
    • Organizer
      Symposium on harmonic analysis
    • Place of Presentation
      中国 Beijing Normal University
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Very slowly increasing functions, Harmonic Analysis and its Applications2012

    • Author(s)
      Eiichi Nakai
    • Organizer
      Harmonic Analysis and its Applications
    • Place of Presentation
      中国 Beijing University of Aeronautics and Astronautics
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Morrey-Campanato spaces2012

    • Author(s)
      Eiichi Nakai
    • Organizer
      Symposium on harmonic analysis
    • Place of Presentation
      中国 Beijing Normal University
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Morrey spaces with variable exponent and variable growth condition2012

    • Author(s)
      Eiichi Nakai
    • Organizer
      研究集会「調和解析と非線形偏微分方程式」
    • Place of Presentation
      京都大学 数理解析研究所
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Generalized Morrey spaces and generalized fractional integrals2012

    • Author(s)
      Eiichi Nakai
    • Organizer
      International Symposium on Banach and Function Spaces 2012
    • Place of Presentation
      九州工業大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Gagliardo-Nirenberg inequality for generalized Riesz potentials of functions in Musielak-Orlicz spaces2012

    • Author(s)
      水田義弘, 中井英一, 澤野嘉宏, 下村哲
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      九州大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Generalized fractional integrals on martingale Morrey-Campanato spaces2012

    • Author(s)
      貞末岳, 中井英一, 澤野嘉宏
    • Organizer
      実解析学シンポジウム2012
    • Place of Presentation
      茨城大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Weak type Morrey spaces with variable exponents2012

    • Author(s)
      中井英一
    • Organizer
      実解析学シンポジウム2012
    • Place of Presentation
      茨城大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Generalized fractional integrals of variable order2012

    • Author(s)
      Eiichi Nakai
    • Organizer
      Harmonic Analysis and its Applications at Tokyo 2012
    • Place of Presentation
      首都大学東京
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] 変動する指標をもつ関数空間 12012

    • Author(s)
      中井英一
    • Organizer
      調和解析セミナー
    • Place of Presentation
      東京大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] 変動する指標をもつ関数空間 22012

    • Author(s)
      中井英一
    • Organizer
      調和解析セミナー
    • Place of Presentation
      東京大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] 変動する指標をもつ関数空間 32012

    • Author(s)
      中井英一
    • Organizer
      調和解析セミナー
    • Place of Presentation
      東京大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Remarks] 研究業績一覧(中井英一)

    • URL

      http://enakai.sci.ibaraki.ac.jp/publication-j.html

    • Related Report
      2014 Annual Research Report
  • [Remarks] 研究業績一覧 ( 中井英一 )

    • URL

      http://enakai.sci.ibaraki.ac.jp/publication-j.html

    • Related Report
      2013 Research-status Report
  • [Remarks] 研究業績一覧 ( 中井英一 )

    • URL

      http://enakai.sci.ibaraki.ac.jp/publication-j.html

    • Related Report
      2012 Research-status Report

URL: 

Published: 2013-05-31   Modified: 2019-07-29  

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