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2014 Fiscal Year Final Research Report

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

Research Project

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Project/Area Number 24540159
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionIbaraki 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

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Published: 2016-06-03  

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