Study on null forms in global space-time in the framework of equalities

2019 Fiscal Year Final Research Report

• Project/Area Number: 16K13771
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Mathematical analysis
• Research Institution: Waseda University
• Principal Investigator: Ozawa Tohru 早稲田大学, 理工学術院, 教授 (70204196)
• Co-Investigator(Kenkyū-buntansha): 田中 和永 早稲田大学, 理工学術院, 教授 (20188288) ; BEZ NEAL 埼玉大学, 理工学研究科, 准教授 (30729843)
• Project Period (FY): 2016-04-01 – 2020-03-31
• Keywords: 関数方程式 / 調和解析 / 実解析 / 変分解析

Outline of Final Research Achievements

Stability of trace theorems on the sphere is studied as the most fundamental subject in the research of null forms in global space-time. We have established the desired optimal inequalities for the stability theory and given its characterization from the viewpoint of duality. Regarding the Hardy and Rellich inequalities, we have formulated their equality framework with explicit remainder terms, therely we were able to recast the associated best constants and extremizers in a direct and explicit understanding. This provides a new method, independent of implicit arguments of contradiction and compactness.

Free Research Field

数学解析

Academic Significance and Societal Importance of the Research Achievements

零形式の時空大域的研究の基盤を揺ぎ無いものとするとともに、函数不等式の従来の理解を、不等式ではなく、等式の枠組みで具体的に与えることができた。