Study of the operators on some function spaces in harmonic analysis

2016 Fiscal Year Final Research Report

• Project/Area Number: 26400129
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Yamagata University
• Principal Investigator: SATO ENJI 山形大学, 理学部, 名誉教授 (80107177)
• Co-Investigator(Renkei-kenkyūsha): KOBAYASHI Masaharu 北海道大学, 理学研究院, 准教授 (30516480)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 分数冪積分作用素 / モレー空間 / フーリエマルチプライヤー / モジュレーション空間 / 双線形作用素

Outline of Final Research Achievements

Study of the operators in function spaces by harmonic analysis is very effective for partial differentiable equations. Moreover, it is important that an operator in some function spaces is bounded. Main subjects in our research are study of Fourier multiplier operators, study of fractional integral operators in Morrey spaces, and study of modulation spaces which are related to partial differential equations. First, we gave a simple proof of the restriction theorem of Fourier multipliers, and generalized the result of the fractional integral operators in Morrey spaces. Also we developed the result in modulation spaces by the study of operating functions.

Free Research Field

数物系科学