Harmonic analysis based on function spaces with variable exponent and its applications

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540159
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Ibaraki University
• Principal Investigator: NAKAI Eiichi 茨城大学, 理学部, 教授 (60259900)
• Co-Investigator(Kenkyū-buntansha): HORIUCHI Toshio 茨城大学, 理学部, 教授 (80157057) ; SOBUKAWA Takuya 早稲田大学, グローバルエデュケーションセンター, 教授 (60252946) ; SADASUE Gaku 大阪教育大学, 教育学部, 准教授 (40324884) ; SAWANO Yoshihiro 首都大学東京, 理工学研究科, 准教授 (40532635)
• Co-Investigator(Renkei-kenkyūsha): MIZUTA Yoshihiro 広島工業大学, 工学部, 教授 (00093815)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 調和解析学 / 実解析学 / 関数空間 / 変動指数 / 分数べき積分 / 特異積分

Outline of Final Research Achievements

We established the theory of Hardy spaces with variable exponent and Orlicz-Hardy spaces, characterizing by Poisson integral, atomic decomposition, Littlewood-Paley decomposition, etc, proving the boundedness of singular and fractional integral operators, and studying related function spaces and their duals. Moreover, we developed the theory of generalized Morrey-Campanato spaces, B_sigma-Morrey-Campanato spaces, and their unified spaces as function spaces with variable oscillation and variable growth conditions. Using these function spaces, we analyzed the properties of solutions of some partial differential equations. Furthermore, we constructed the harmonic analysis theory for martingales.

Free Research Field

数学、解析学