Study of singular integrals and function spaces

• Project/Area Number: 21540199
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Tokai University
• Principal Investigator: FURUYA Yasuo 東海大学, 沼津教養教育センター, 教授 (70234903)
• Co-Investigator(Kenkyū-buntansha): NARASAKI Takashi 東海大学, 理学部, 教授 (70119692) ; MATSUYAMA Tokio 中央大学, 理工学部, 教授 (70249712)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 特異積分 / ハーディー空間 / Morrey空間 / Herz空間 / 多重線形作用素 / weight / fractional integral

Research Abstract

We study boundedness of generalized singular integral operators on several function spaces, in particular, on Hardy space, Morrey space and Herz space. We also study multilinear singular interals and weighted estimates.

Research Products

• [Journal Article] The Adams inequality on weighted Morrey spaces (2011)
  • Author(s): T. Iida, Yasuo Komori-Furuya and E. Sato
  • Journal Title: Tokoyo J. Math. Volume: vol.34 Pages: 535-545
  • Peer Reviewed
• [Journal Article] A note on Muckenhoupt type weight classes on nondoubling measure spaces (2011)
  • Author(s): Yasuo Komori-Furuya
  • Journal Title: Georgian Math. J. Volume: vol.18 Pages: 131-135
  • Peer Reviewed
• [Journal Article] Fractional integral operators on Herz spaces (2011)
  • Author(s): Yasuo Komori-Furuya
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: vol.26 Pages: 15-22
  • Peer Reviewed
• [Journal Article] Two remarks on commutators of Hardy operators (2011)
  • Author(s): Yasuo Komori-Furuya
  • Journal Title: Australian J. of Math. Anal. and Appl Volume: vol.7 Pages: 1-5
  • Peer Reviewed
• [Journal Article] Fractional integral operators on Herz spaces for supercritical indices (2011)
  • Author(s): Yasuo Komori-Furuya
  • Journal Title: J. Funct. Spaces and Appl. Volume: vol.9 Pages: 179-190
  • Peer Reviewed
• [Journal Article] Commutators of pseudo-differential operators on local Hardy spaces (2011)
  • Author(s): Yasuo Komori-Furuya
  • Journal Title: Acta Sci. Math. Volume: vol.77 Pages: 489-501
  • Peer Reviewed
• [Journal Article] Commutators of pseudo-differential operators on local Hardy spaces (2011)
  • Author(s): Yasuo Komori-Furuya
  • Journal Title: Acta Sci.Math.(Szeged) Volume: 82 Pages: 375-385
  • Peer Reviewed
• [Journal Article] Fractional integral operators on Herz spaces for supercritical indices (2011)
  • Author(s): Yasuo Komori-Furuya
  • Journal Title: J.Funct.Spaces and Appl. Volume: 9 Pages: 179-190
  • Peer Reviewed
• [Journal Article] Two remarks on commutators of Hardy operators (2011)
  • Author(s): Yasuo Komori-Furuya
  • Journal Title: Australian J.of Math.Anal.and Appl. Volume: 7 Pages: 1-5
  • Peer Reviewed
• [Journal Article] A note on Muckenhoupt type weight classes on nondoubling measure spaces (2011)
  • Author(s): Yasuo Komori-Furuya
  • Journal Title: Georgian Math.J. Volume: 18 Pages: 131-135
  • Peer Reviewed
• [Journal Article] The Adams inequality on weighted Morrey spaces (2011)
  • Author(s): Takeshi IIa, Yasuo Komori-Furuya, Enji Sato
  • Journal Title: Tokoyo J.Math. Volume: 34 Pages: 535-545
  • Peer Reviewed
• [Journal Article] Global well-posedness for the exterior initial-boundary value problem to the Kirchhoff equation (2010)
  • Author(s): Tokio Matsuyama
  • Journal Title: J. Math. Soc. Japan Volume: vol.62 Pages: 1167-1204
  • NAID: 10027871075
  • Peer Reviewed
• [Journal Article] Strong and weak estimates for fractional integral operators on some Herz-type function spaces (2010)
  • Author(s): Yasuo Komori and Katsuo Matsuoka
  • Journal Title: Rendiconti del Circolo Math. di Palermo Volume: vol.82 Pages: 375-385
  • Peer Reviewed
• [Journal Article] Weighted estimates for singular integral operators on CMO spaces (2010)
  • Author(s): Yasuo Komori-Furuya and K. Matsuoka
  • Journal Title: Sci. Math. Japonicae Volume: vol.72 Pages: 219-226
  • Peer Reviewed
• [Journal Article] A note on multilinear fractional integrals (2010)
  • Author(s): T. Iida, Yasuo Komori-Furuya and E. Sato
  • Journal Title: Analysis in Theory and Applications Volume: Vol.26 Pages: 301-307
  • Peer Reviewed
• [Journal Article] Asymptotic integration and dispersion for hyperbolic equations (2010)
  • Author(s): Tokio Matsuyama and M. Ruzhansky
  • Journal Title: Advanced in Differential Equations Volume: vol.15 Pages: 721-756
  • Peer Reviewed
• [Journal Article] Some weak-type estimates for singular integral operators on CMO spaces (2010)
  • Author(s): Y.Komori-Furuya, K.Matsuoka
  • Journal Title: Hokkaido Math.J. Volume: 39 Pages: 115-126
  • Peer Reviewed
• [Journal Article] Weighted estimates for singular integral operators on CMO spaces (2010)
  • Author(s): Y.Komori-Furuya, K.Matsuoka
  • Journal Title: Sci.Math.Japonica Volume: 72 Pages: 219-226
  • Peer Reviewed
• [Journal Article] Strong and weak estimates for fractional integral operators on some Herz-type functions spaces (2010)
  • Author(s): Y.Komori-Furuya, K.Matsuoka
  • Journal Title: Rendiconti del Circolo Math.di Palermo Volume: 82 Pages: 375-385
  • Peer Reviewed
• [Journal Article] Nondoubling Measure and Harmonic Analysis (2010)
  • Author(s): Y.Komori
  • Journal Title: American Mathematical Society Translations, Selected Papers on Analysis and Differential Equations Volume: 230 Pages: 87-106
  • NAID: 10026415522
  • Peer Reviewed
• [Journal Article] Global well-posedness for the exterior initial-boundary value problem to the Kirchhoff equation (2010)
  • Author(s): T.Matsuyama
  • Journal Title: J.Math.Society Japan Volume: 62 Pages: 1167-1204
  • NAID: 10027871075
  • Peer Reviewed
• [Journal Article] Asymptotic integration and dispersion for hyperbolic equations (2010)
  • Author(s): T.Matsuyama, M.Ruzhansky
  • Journal Title: Advances in Differential Equations 15 Pages: 721-756
  • Peer Reviewed
• [Journal Article] Time decay for hyperbolic equations with homogeneous symbols (2009)
  • Author(s): Tokio Matsuyama and M. Ruzhansky
  • Journal Title: Comptes Rendus Acad. Sci. Paris, Ser. I Volume: Vol.347 Pages: 915-919
  • Peer Reviewed
• [Journal Article] Boundedness of several operators on weighted Herz spaces (2009)
  • Author(s): Yasuo Komori
  • Journal Title: J. Funct. Sp. and Appl. Volume: vol.7 Pages: 1-12
  • Peer Reviewed
• [Journal Article] Nondoubling measureと調和解析 (2009)
  • Author(s): 小森康雄
  • Journal Title: 数学 Volume: 61巻 Pages: 376-394
  • NAID: 10026415522
  • Peer Reviewed
• [Journal Article] Boundedness of several operators on weighted Herz spaces (2009)
  • Author(s): Yasuo Komori
  • Journal Title: Journal of Funetion Spaces and Applications 7 Pages: 1-12
  • Peer Reviewed
• [Journal Article] Nondoubling measureと調和解析 (2009)
  • Author(s): 小森康雄
  • Journal Title: 数学 61 Pages: 376-394
  • NAID: 10026415522
  • Peer Reviewed
• [Journal Article] Time decay for hyperbolic equations with homogeneous symbols (2009)
  • Author(s): Tokio Matsuyama, M.Ruzhansky
  • Journal Title: Comptes Rendus Acad. Sci. Paris, Ser. I 347 Pages: 915-919
  • Peer Reviewed
• [Presentation] Global solutions to Kirchhoff systems (2012)
  • Author(s): 松山登喜夫
  • Organizer: 早稲田大学応用解析研究会
  • Place of Presentation: 早稲田大学
  • Year and Date: 2012-11-19
• [Presentation] Asymptotic properties for hyperbolic systems with time-dependent coefficients (2012)
  • Author(s): Tokio Matsuyama
  • Organizer: 8th International ISAAC Congress, Moscow
  • Place of Presentation: People's Friendship University of Russia
  • Year and Date: 2012-08-25
• [Presentation] Integral operators on BσMorrrey-Campanato spaces (2012)
  • Author(s): 古谷康雄, 松岡勝男, 中井英一, 澤野嘉宏
  • Organizer: 日本数学会年会
  • Place of Presentation: 東京理科大学
  • Year and Date: 2012-03-29
• [Presentation] Integral operators on Bσ Morrrey-Campanato spaces (2012)
  • Author(s): 古谷康雄, 松岡勝男, 中井英一, 澤野嘉宏
  • Organizer: 日本数学会年会
  • Place of Presentation: 東京理科大学
  • Year and Date: 2012-03-29
• [Presentation] Global solutions to Kirchhoff systems (2012)
  • Author(s): 松山登喜夫
  • Organizer: 発展方程式シンポジウム
  • Place of Presentation: 東海大学
  • Year and Date: 2012-03-08
• [Presentation] Maximal functionの弱L^p有界性 (2011)
  • Author(s): 古谷康雄
  • Organizer: 調和解析セミナー
  • Place of Presentation: 大阪大学
  • Year and Date: 2011-12-16
• [Presentation] Global solutions to Kirchhoff systems (2011)
  • Author(s): 松山登喜夫
  • Organizer: 早稲田大学応用解析研究会
  • Place of Presentation: 早稲田大学理工学術院
  • Year and Date: 2011-11-19
• [Presentation] Dispersion for 3D wave equation with a potential in exterior domains (2011)
  • Author(s): Tokio Matsuyama
  • Organizer: Asymptotic Properties of Solutions to Hyperbolic Equations
  • Place of Presentation: Imperial College London
  • Year and Date: 2011-03-23
• [Presentation] New multiple weights and the Adams inequality on weighted Morrey spaces (2010)
  • Author(s): 飯田毅士, 古谷康雄, 佐藤圓治
  • Organizer: 調和解析セミナー
  • Place of Presentation: 日本大学
  • Year and Date: 2010-12-26
• [Presentation] Dispersion for 3D wave equation with a potential in a exterior domain (2010)
  • Author(s): 松山登喜夫
  • Organizer: 微分方程式の総合的研究
  • Place of Presentation: 京都大学
  • Year and Date: 2010-12-18
• [Presentation] Dispersion for 3D wave equation with a potential in an exterior domain (2010)
  • Author(s): 松山登喜夫
  • Organizer: 微分方程式の総合的研究
  • Place of Presentation: 京都大学
  • Year and Date: 2010-12-18
• [Presentation] The Laplace equation on Lipschitz domains(Kenigらの仕事の紹介) (2010)
  • Author(s): 古谷康雄
  • Organizer: 偏微分方程式の諸問題
  • Place of Presentation: 東海大学
  • Year and Date: 2010-10-20
• [Presentation] The Adams inequality on weighted Morrey spaces (2010)
  • Author(s): 飯田毅士, 古谷康雄, 佐藤圓治
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-09-26
• [Presentation] Fractional integral operators on Herz spaces for supercritical indices (2010)
  • Author(s): 古谷康雄
  • Organizer: 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
  • Year and Date: 2010-07-06
• [Presentation] Cauchy problem for the system for damped wave equations with slowly decaying data (2010)
  • Author(s): 楢崎隆
  • Organizer: 発展方程式シンポジウム
  • Place of Presentation: 東海大学
  • Year and Date: 2010-03-12
• [Presentation] Cauchy problem for the system of damped wave equations with slowly decayine data (2010)
  • Author(s): 楢崎隆
  • Organizer: 発展方程式シンポジウム
  • Place of Presentation: 東海大学
  • Year and Date: 2010-03-12
• [Presentation] 多重線形特異積分入門 (2009)
  • Author(s): 古谷康雄
  • Organizer: 調和解析セミナー
  • Place of Presentation: 岡山大学
  • Year and Date: 2009-12-25
• [Presentation] Pseudo-differential operators on Hardy spaces (2009)
  • Author(s): 古谷康雄
  • Organizer: 偏微分方程式の諸問題
  • Place of Presentation: 東海大学
  • Year and Date: 2009-10-23
• [Presentation] nondoubling測度空間上のweightに関する注意 (2009)
  • Author(s): 古谷康雄
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-25
• [Presentation] Nondoubling測度空間上のweightに関する注意 (2009)
  • Author(s): 古谷康雄
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-25
• [Presentation] Kirchhoff equation in an exterior domain (2009)
  • Author(s): Tokio Matsuyama
  • Organizer: GF2009
  • Place of Presentation: Wien University
  • Year and Date: 2009-09-03
• [Presentation] Strichartz estimates for wave equation with a potential in an exterior domain (2009)
  • Author(s): Tokio Matsuyama
  • Organizer: ISAAC Congress 2009
  • Place of Presentation: Imperial College London
  • Year and Date: 2009-06-17
• [Presentation] Strichartz estimates for wave equation with a potential in an exterior Domain (2009)
  • Author(s): T.Matsuyama
  • Organizer: ISAAC Congress 2009
  • Place of Presentation: Imperial College London
  • Year and Date: 2009-06-17