Potential Analysis for parabolic Hardy spaces

2014 Fiscal Year Final Research Report

• Project/Area Number: 22540209
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Meijo University
• Principal Investigator: SUZUKI Noriaki 名城大学, 理工学部, 教授 (50154563)
• Co-Investigator(Renkei-kenkyūsha): NISHIO Masaharu 大阪市立大学, 大学院理学研究科, 准教授 (90228156) ; YAMADA Masahiro 岐阜大学, 教育学部, 教授 (00263666) ; SHIMOMURA Katsunori 茨城大学, 理学部, 教授 (00101559)
• Research Collaborator: NAKAGAWA Hayato ; SAKAI Ryozi ; ITO Kentaro
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: ポテンシャル解析 / 放物型作用素 / ベルグマン空間 / ハーディ空間

Outline of Final Research Achievements

Potential theory is mainly studied solutions of elliptic operators, however, analysis of parabolic operators is also interesting topics, which is called parabolic potential theory. In this view point, we study Hardy and Bergman spaces with respect to a parabolic operators by using parabolic potential analysis. A characterization for positive measures whose Carleson inclusion are bounded is obtained. On Bergamn spaces, we discuss that when Toeplitz operator is bounded, compact, of Schatten class or of finite rank. We also study a relation between Toepliz operator and Carleson inclusion.

Free Research Field

ポテンシャル論