Boundedness of multilinear pseudo-differential operators

2023 Fiscal Year Final Research Report

• Project/Area Number: 20K14339
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 12020:Mathematical analysis-related
• Research Institution: Gifu University (2023); Gunma University (2020-2022)
• Principal Investigator: KATO Tomoya 岐阜大学, 工学部, 准教授 (40847026)
• Project Period (FY): 2020-04-01 – 2024-03-31
• Keywords: 擬微分作用素 / フーリエ乗子作用素 / 多重線形作用素 / 関数空間

Outline of Final Research Achievements

Pseudo-differential operators are one of generalization of partial differential operators. Multilinear analogues are its extension to operating to products of functions, which have been studied extensively. In this research, we concentrated on generalizing conditions to assure the boundedness of multilinear pseudo-differential operators and tried to give improvement or refinement of known results. In particular, we extended conditions how fast symbols of the operators decay far from the origin to more general ones and also weaken derivative assumptions of symbols.

Free Research Field

実解析学

Academic Significance and Societal Importance of the Research Achievements

本研究では主に，S_{0,0}型のシンボルをもつ多重線形擬微分作用素について考察を行った．このシンボルは，微分によって減衰度を変えないというものである．この作用素の有界性に関する結果は，2000年初頭にBenyiらによって始まり，2010年頃にMiyachi-Tomitaによって基本的な枠組みでの研究は完結していた．本研究によって，それらをさらに拡張したことで，今後の新たな研究の枠組みを作ることができたのだとしたら嬉しく思う．