Investigation of function spaces of solutions of parabolic equations

• Project/Area Number: 25400133
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Gifu University
• Principal Investigator: Yamada Masahiro 岐阜大学, 教育学部, 教授 (00263666)
• Co-Investigator(Renkei-kenkyūsha): Hishikawa yosuke 岐阜大学, 教育学部, 助教 (50585081) ; Yamamoto Takanori 北海学園大学, 工学部, 教授 (60182630) ; Nishio Masaharu 大阪市立大学, 理学研究科, 准教授 (90228156)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 放物型ハーディー空間 / 放物型ブロッホ空間 / 放物型共役調和関数 / 双対空間 / 基本解 / 積分作用素 / 境界極限存在定理 / 拡張関数 / 放物型極大関数 / 放物型共役関数 / 放物型ハーディー空間上の作用素

Outline of Final Research Achievements

We study properties of α-parabolic conjugate functions. We introduce the notion of conjugacy to α-parabolic Bergman spaces. In this study, we define α-parabolic conjugate functions of parabolic Hardy spaces. Study of α-parabolic conjugate functions of parabolic Hardy spaces is diffcult for the case of p-1. Therefore, we study α-parabolic Bloch spaces and give an application to the estimates of tangential derivative norms.

Research Products

• [Journal Article] Fractional calculus and L^{α}-conjugates on parabolic Hardy spaces (2015)
  • Author(s): Hishikawa, Yosuke; Nishio, Masaharu; Yamada, Masahiro
  • Journal Title: Scientiae Mathematicae Japonicae Volume: 77 Pages: 371-391
  • Peer Reviewed
• [Journal Article] L(\alpha)-conjugates on parabolic Bergman spaces (2014)
  • Author(s): YOSUKE HISHIKAWA, MASAHARU NISHIO, AND MASAHIRO YAMADA
  • Journal Title: Potential Analysis Volume: 40 Pages: 525-537
  • Peer Reviewed
• [Journal Article] FRACTIONAL CALCULUS AND L{\alpha}-CONJUGATES ON PARABOLIC HARDY SPACES (2013)
  • Author(s): YOSUKE HISHIKAWA, MASAHARU NISHIO, AND MASAHIRO YAMADA
  • Journal Title: Scientiae Mathematicae Japonicae(on line) Volume: 26 Pages: 687-707
  • Peer Reviewed
• [Presentation] L^{α}-conjugates on parabolic Bloch spaces (2016)
  • Author(s): 菱川洋介，西尾昌治，山田雅博
  • Organizer: 日本数学会
  • Place of Presentation: 筑波大学
  • Year and Date: 2016-03-16
• [Presentation] L^{α}-conjugates on parabolic Bloch spaces (2015)
  • Author(s): 菱川洋介，西尾昌治，山田雅博
  • Organizer: ポテンシャル論研究集会
  • Place of Presentation: 名城大学サテライトキャンパス
  • Year and Date: 2015-09-22
• [Presentation] 放物型ハーディー空間における放物型共役関数 (2014)
  • Author(s): 西尾昌治，菱川洋介，山田雅博
  • Organizer: ポテンシャルセミナー
  • Place of Presentation: 岐阜大学（岐阜県岐阜市）
  • Year and Date: 2014-11-02 – 2014-11-03
• [Presentation] 放物型ハーディ空間とエリア関数 (2013)
  • Author(s): 西尾昌治，菱川洋介，山田雅博
  • Organizer: ２０１３年度ポテンシャル論研究集会
  • Place of Presentation: 北海道大学