Study of singular integrals and Triebel-Lizorkin spaces associated to surfaces

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04942
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kwansei Gakuin University
• Principal Investigator: YABUTA KOZO 関西学院大学, 数理科学研究センター, 客員研究員 (30004435)
• Co-Investigator(Kenkyū-buntansha): 北原 和明 関西学院大学, 理工学部, 教授 (40195277)
• Co-Investigator(Renkei-kenkyūsha): SATO SHUUICHI 金沢大学, 人間社会研究域学校教育系, 教授 (20162430)
• Research Collaborator: DING Yong 北京師範大学, 数学科学学院, 教授 ; XUE Qingying 北京師範大学, 数学科学学院, 教授
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 調和解析 / フーリエ解析 / 実解析 / 函数解析

Outline of Final Research Achievements

For singular integrals with kernel associated to the surface of the form {x=Ψ(|y|)} etc, we obtained several good estimates in Triebel-Lizorkin spaces and Besov spaces. We published 14 results for singular integrals with rough kernel, vector space valued singular integrals, multilinear singular integrals, and maximal singular intefrals. These contribute to the development of the study of singular integrals.

Free Research Field

数学