A study of singular integral operators

• Project/Area Number: 15K04938
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Tokai University
• Principal Investigator: Furuya Yasuo 東海大学, 理学部, 教授 (70234903)
• Co-Investigator(Kenkyū-buntansha): 澤野 嘉宏 首都大学東京, 理工学研究科, 准教授 (40532635) ; 松山 登喜夫 中央大学, 理工学部, 教授 (70249712)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000); Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 特異積分 / ハーディー空間 / 多重線形作用素 / モレイ空間 / 分数べき作用素 / モレー空間 / Morrey 空間 / 分数べき積分作用素 / 重みつき評価

Outline of Final Research Achievements

We consider the boundedness of singular integral operators. In particular we study multilinear fractional operators and obtain the strong type estimates on product of Lebesgue spaces at critical indices. We also improve bilinear Stein-Weiss inequality.

Research Products

• [Journal Article] Weighted estimates for fractional integral operators on central Morrey spaces (2017)
  • Author(s): Ｙａｓｕｏ Ｋｏｍｏｒｉ－Ｆｕｒｕｙａ ａｎｄ Ｅｎｊｉ Ｓａｔｏ
  • Journal Title: Ｍａｔｈ． Ｎａｃｈｒ． Volume: ２９０
  • Peer Reviewed
• [Journal Article] Fractional integral operators on central Morrey spaces (2017)
  • Author(s): Y.Komori-Furuya, E.Sato
  • Journal Title: Math. Inequal. Appl. Volume: 20 Issue: 3 Pages: 801-813
  • DOI: 10.7153/mia-20-50
  • Peer Reviewed
• [Journal Article] Notes on endpoint estimates for multilinear fractional integral operators (2017)
  • Author(s): Yasuo Komori-Furuya
  • Journal Title: Proceedings of American MathematicalSociety Volume: 145 Issue: 4 Pages: 1515-1526
  • DOI: 10.1090/proc/13389
  • Peer Reviewed
• [Journal Article] Ｌｏｃａｌ ｇｏｏｄ ｌａｍｂｄａ ｅｓｔｉｍａｔｅ ｆｏｒ ｔｈｅ ｓｈａｒｐ ｍａｘｉｍａｌ ｆｕｎｃｔｉｏｎ ａｎｄ ｗｅｉｇｈｔｅｄ Ｍｏｒｒｅｙ ｓｐａｃｅ (2015)
  • Author(s): Ｙａｓｕｏ Ｋｏｍｏｒｉ－Ｆｕｒｕｙａ
  • Journal Title: Ｊ． Ｆｕｎｃｔｉｏｎ Ｓｐａｃｅｓ Volume: ２０１５
  • Peer Reviewed
• [Presentation] An inequality which interpolates Adams and Spanne (2015)
  • Author(s): Ｙａｓｕｏ Ｋｏｍｏｒｉ－Ｆｕｒｕｙａ
  • Organizer: Harmonic Analysis and its Applications in Tokyo 2015
  • Place of Presentation: 早稲田大学
  • Year and Date: 2015-11-27
  • Invited