Reseach on multilinear harmonic analysis and its applications

• Project/Area Number: 20540149
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Hokkaido University
• Principal Investigator: TACHIZAWA Kazuya 北海道大学, 大学院・理学研究院, 准教授 (80227090)
• Co-Investigator(Kenkyū-buntansha): HAYASHI Mikihiro 北海道大学, 大学院・理学研究院, 教授 (40007828)
• Co-Investigator(Renkei-kenkyūsha): HORIUCHI Toshio 茨城大学, 理学部, 教授 (80157057)
• Project Period (FY): 2008 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 調和解析 / 多重線形 / ウェーブレット / 実解析 / 多重線形作用素 / 関数空間

Research Abstract

As an example of multilinear operators we studied multilinear pseudo-differential operators. In particular we got a condition of the symbol of multilinear pseudo-differential operators defined on products of a Hilbert space, which belong to the Schatten-von Neumann class. Moreover we provided the wavelet characterization of the weighted Herz spaces. Moreover we proved the Sobolev-Lieb-Thirring inequality with respect to the Bessel potentials by means of the wavelet characterization of weighted Lp spaces.

Research Products

• [Journal Article] The Caffarelli-Kohn-Nirenberg type inequalities involving critical and supercritical weights, Proc. (2012)
  • Author(s): Toshio Horiuchi and Peter Kumlin
  • Journal Title: Japan Acad. Ser.A Math. Sci Volume: 88(1) Pages: 1-6
  • Peer Reviewed
• [Journal Article] Wavelet characterization of weighted spaces (2010)
  • Author(s): Kazuya Tachizawa
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: B22 Pages: 61-70
  • Peer Reviewed
• [Journal Article] Wavelet characterization of weighted spaces (2010)
  • Author(s): Kazuya Tachizawa
  • Journal Title: RIMS Kokyuroku Bessatsu B22 Pages: 61-70
  • Peer Reviewed
• [Journal Article] Wavelet characterization of weighted spaces (2010)
  • Author(s): Kazuya Tachizawa
  • Journal Title: BIMS Kokyuroku Bessatsu Volume: B22 Pages: 61-70
  • Peer Reviewed
• [Journal Article] Wavelet characterization of weighted spaces (2010)
  • Author(s): Kazuya Tachizawa
  • Journal Title: RIMS Kokyuroku Bessatsu (掲載決定)
  • Peer Reviewed
• [Journal Article] Schatten-von Neumann classes of multilinear pseudodifferential operators (2009)
  • Author(s): Kazuya Tachizawa
  • Journal Title: 研究集会Harmonic analysis and its applications at Tokyo 2008 報告集 Pages: 114-122
• [Journal Article] Wavelet characterizations of weighted spaces (2009)
  • Author(s): Kazuya Tachizawa
  • Journal Title: RIMS Kokyuroku Bessatsu (掲載確定)
  • Peer Reviewed
• [Journal Article] Wavelet characterizations of weighted Herz spaces (2008)
  • Author(s): Mitsuo Izuki and Kazuya Tachizawa
  • Journal Title: Scientiae Mathematicae Japonicae Volume: 67(3) Pages: 353-363
  • NAID: 10021089666
  • Peer Reviewed
• [Journal Article] Kato's inequalities for degenerate quasilinear lliptic operators (2008)
  • Author(s): Toshio Horiuchi
  • Journal Title: Kyungpook Mathematical Journal Volume: 48(1) Pages: 15-21
  • Peer Reviewed
• [Journal Article] Wavelet characterizations of weighted Herz spaces (2008)
  • Author(s): Mitsuo Izuki, Kazuya Tachizawa
  • Journal Title: Scientiae Mathematicae Japonicae 67(3) Pages: 353-363
  • NAID: 10021089666
  • Peer Reviewed
• [Journal Article] Kato's inequalities for degenerate quasilinear elliptic operators (2008)
  • Author(s): Toshio Horiuchi
  • Journal Title: Kyungpook Mathematical Journal 48(1) Pages: 15-24
  • Peer Reviewed
• [Journal Article] Wavelelet characterizations of weighted Herz spaces (2008)
  • Author(s): Mitsuo Izuki
  • Journal Title: Scientiae Mathematicae Japonicae 67 Pages: 353-363
  • Peer Reviewed
• [Presentation] Schatten-von Neumann classes of pseudodifferential operators (2008)
  • Author(s): Kazuya Tachizawa
  • Organizer: 研究集会Harmonic Analysis and its Applications at Tokyo 2008
  • Place of Presentation: 首都大学東京
  • Year and Date: 2008-10-11
• [Presentation] Schatten-von Neumann classes of pseudodifferential operators (2008)
  • Author(s): Kazuya Tachizawa
  • Organizer: 研究集会 Harmonic Analysis and its Applications at Tokyo 2008
  • Place of Presentation: 首都大学東京
  • Year and Date: 2008-10-11
• [Presentation] Schatten-von Neumann classes of pseudoclifferentia operators (2008)
  • Author(s): Kazuya Tachizawa
  • Organizer: Harmonic Analysiss and its Applications at Tokyo 2008
  • Place of Presentation: 首都大学東京
  • Year and Date: 2008-10-11