A real analytic study on wavelets and variable exponent analysis

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540185
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Okayama University (2014); Tokyo Denki University (2012-2013)
• Principal Investigator: IZUKI Mitsuo 岡山大学, 教育学研究科(研究院), 講師 (80507179)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 変動指数 / BMO

Outline of Final Research Achievements

One of the main results is generalization of the BMO norm using variable exponent. A joint work with Yoshihiro Sawano and Yohei Tsutsui has showed the following: The generalization is possible, provided that a variable exponent guarantees the weak boundedness of the Hardy-Littlewood maximal operator. The second main result is concerning with the study on various function spaces with variable exponents. A joint work with Eiichi Nakai and Yoshihiro Sawano has characterized variable Lebesgue spaces with variable exponent equipped a weight satisfying the variable exponent Muckenhoupt condition. Moreover a joint work with Takahiro Noi has clarified the dual spaces of
Herz, Besov and Triebel-Lizorkin spaces with variable exponents.

Free Research Field

実解析学