Structures of some martingale spaces, and operators on these martingale spaces

• Project/Area Number: 24540171
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Osaka Kyoiku University
• Principal Investigator: SADASUE Gaku 大阪教育大学, 教育学部, 准教授 (40324884)
• Co-Investigator(Kenkyū-buntansha): NAKAI Eiichi 茨城大学, 理学部, 教授 (60259900)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000); Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: マルティンゲール / モリー･カンパナート空間 / 分数べき積分作用素 / 最大関数 / BMO空間 / カンパナート空間 / 一般化分数べき作用素 / バナッハ関数空間 / ヘルツ型不等式 / BMO 空間 / 分数べき積分 / モリー空間

Outline of Final Research Achievements

The notion of martingale, which was established in probability theory as an abstraction of fairness of games, is important in real analysis through the similarity between martingale spaces and function spaces. We study this similarity and obtain the structure of martingale Morrey-Campanato space and the boundedness of fractional integral operators. Besides, we obtain a necessary and sufficient condition for the boundedness of pointwise multiplier. Using this condition, we obtain the boundedness of the maximal functions on spaces with variable exponents and on martingale BMO spaces.

Research Products

• [Journal Article] Pointwise multipliers on martingale Campanato spaces (2014)
  • Author(s): Eiichi Nakai and Gaku Sadasue
  • Journal Title: Studia Mathematica Volume: 220 Issue: 1 Pages: 87-100
  • DOI: 10.4064/sm220-1-5
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Martingale Morrey-Hardy and Campanato-Hardy Spaces (2013)
  • 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
  • Peer Reviewed
• [Journal Article] Maximal function on generalized martingale Lebesgue spaces with variable exponent (2013)
  • 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
  • Peer Reviewed
• [Journal Article] Martingale Morrey-Campanato spaces and fractional integrals (2012)
  • 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
  • Peer Reviewed
• [Presentation] A note on Herz type inequalities (2014)
  • Author(s): 貞末 岳
  • Organizer: 実解析学シンポジウム 2014
  • Place of Presentation: 富山大学
  • Year and Date: 2014-11-02
• [Presentation] Maximal functions on generalized martigale Lebesgue spaces with variable exponent
  • Author(s): 中井 英一・貞末 岳
  • Organizer: 日本数学会
  • Place of Presentation: 愛媛大学
• [Presentation] A note on BLO martingales
  • 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
• [Presentation] A characterization of BLO martingales
  • Author(s): 中井 英一・貞末 岳
  • Organizer: 日本数学会
  • Place of Presentation: 学習院大学
• [Presentation] マルティンゲール空間の解析学
  • Author(s): 貞末 岳
  • Organizer: 第５１回実関数論・函数解析学合同シンポジウム
  • Place of Presentation: 東京理科大学森戸記念館
  • Invited
• [Presentation] Generalized fractional integrals on martingale Morrey-Campanato spaces
  • Author(s): 中井 英一・貞末 岳・澤野 嘉宏（講演者：貞末 岳）
  • Organizer: 実解析学シンポジウム 2012
  • Place of Presentation: 茨城大学理学部
• [Presentation] Generalized Morrey-Campanato spaces of martingales
  • Author(s): 中井 英一・貞末 岳・澤野 嘉宏（講演者：貞末 岳）
  • Organizer: 日本数学会
  • Place of Presentation: 京都大学