A study of singular integrals and function spaces

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540194
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Tokai University
• Principal Investigator: FURUYA Yasuo 東海大学, 理学部, 教授 (70234903)
• Co-Investigator(Kenkyū-buntansha): SAWANO Yoshihiro 首都大学東京, 理工学研究科, 准教授 (40532635) ; MATSYAMA Tokio 中央大学, 理工学部, 教授 (70249712)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: Morrey 空間 / weight / Adams不等式

Outline of Final Research Achievements

We prove the boundedness of multilinear fractional integral operators on product of Herz spaces. We also consider supercritical cases. We introduce new function spaces called B_sigma spaces which unify Morrey spaces and Herz spaces, and prove the boundedness of the Hardy-Littlewood maximaloperator,singular integral operators and fractional integral operators on this space. We obtain the boounded of fractional integral operators on weighted Morrey space. Our result generalizes both Muckenhoupt-Wheeden inequality and Adams inequality.

Free Research Field

実解析学