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

2014 Fiscal Year Final Research Report

• 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
• 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

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.

Free Research Field

確率解析学