Pseudodifferential operators and time-frequency analysis

• Project/Area Number: 21740097
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Osaka University
• Principal Investigator: TOMITA Naohito 大阪大学, 大学院・理学研究科, 准教授 (10437337)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: 調和解析 / 擬微分作用素 / フーリエマルチプライヤー / 多重線形作用素 / 多重線形 / ハーディー空間 / L^p-有界性 / フーリエマルチプライー / モジュレーション空間 / ベソフ空間

Research Abstract

I studied the boundedness of pseudodifferential operators and multilinear Fourier multiplier operators. In particular, I succeeded in weakening the known smoothness conditions to assure the boundedness of them.

Research Products

• [Journal Article] On the L^p-boundedness of pseudo-differential operators with non-regular symbols (2011)
  • Author(s): N. Tomita
  • Journal Title: Arkiv for Matematik Volume: 49 Pages: 175-197
  • Peer Reviewed
• [Journal Article] Remarks on nonlinear operations on modulation spaces (2011)
  • Author(s): M. Sugimoto, N. Tomita and B. Wang
  • Journal Title: Integral Transforms and Special Functions Volume: 22 Pages: 351-358
  • Peer Reviewed
• [Journal Article] Changes of variables in modulation and Wiener amalgam spaces (2011)
  • Author(s): M. Ruzhansky, M. Sugimoto, J. Toft and N. Tomita
  • Journal Title: Mathematische Nachrichten Volume: 284 Pages: 2078-2092
  • Peer Reviewed
• [Journal Article] Remarks on nonlinear operations on modulation spaces (2011)
  • Author(s): M.Sugimoto, N.Tomita, B.Wang
  • Journal Title: Integral Equations and Special Functions Volume: 22 Issue: 4-5 Pages: 351-358
  • DOI: 10.1080/10652469.2010.541054
  • Peer Reviewed
• [Journal Article] A Hormander type multiplier theorem for multilinear operators (2010)
  • Author(s): N. Tomita
  • Journal Title: Journal of Functional Analysis Volume: 259 Pages: 2028-2044
  • Peer Reviewed
• [Journal Article] Unimodular Fourier multipliers on modulation spaces M^{ p, q} for 0<p<1 (2010)
  • Author(s): N. Tomita
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: 18 Pages: 125-132
  • Peer Reviewed
• [Journal Article] On the Hormander multiplier theorem and modulation spaces (2009)
  • Author(s): N. Tomita
  • Journal Title: Applied and Computational Harmonic Analysis Volume: 26 Pages: 408-415
  • Peer Reviewed
• [Journal Article] Embedding relations between local Hardy and modulation spaces (2009)
  • Author(s): M. Kobayashi, A. Miyachi and N. Tomita
  • Journal Title: Studia Mathematica Volume: 192 Pages: 79-96
  • Peer Reviewed
• [Journal Article] Estimates for unimodular Fourier multipliers on modulation spaces (2009)
  • Author(s): A. Miyachi, F. Nicola, S. Rivetti, A. Tabacco and N. Tomita
  • Journal Title: Proceedings of the American Mathematical Society Volume: 137 Pages: 3869-3883
  • Peer Reviewed
• [Journal Article] On the Hormander multiplier theorem and modulation spaces (2009)
  • Author(s): N.Tomita
  • Journal Title: Applied and Computational Harmonic Analysis 26 Pages: 408-415
  • Peer Reviewed
• [Journal Article] Embedding relation between local Hardy and modulation spaces (2009)
  • Author(s): M.Kobayashi, A.Miyachi, N.Tomita
  • Journal Title: Studia Mathematica 192 Pages: 79-96
  • Peer Reviewed
• [Journal Article] Estimates for unimodular Fourier multipliers on modulation spaces (2009)
  • Author(s): A.Miyachi, F.Nicola, S.Rivetti, A.Tabacco, N.Tomita
  • Journal Title: Proceedings of the American Mathematical Society 137 Pages: 3869-3883
  • Peer Reviewed
• [Presentation] Sharp smoothness conditions for bilinear Fourier multipliers (2012)
  • Author(s): 冨田直人, 宮地晶彦
  • Organizer: 日本数学会年会
  • Place of Presentation: 東京理科大学
  • Year and Date: 2012-03-29
• [Presentation] Sharp estimates for bilinear Fourier multipliers (2012)
  • Author(s): 冨田直人
  • Organizer: 松山解析セミナー
  • Place of Presentation: 愛媛大学
  • Year and Date: 2012-02-04
• [Presentation] 双線形フーリエマルチプライヤーが有界作用素になるための滑らかさの条件について (2011)
  • Author(s): 冨田直人
  • Organizer: 調和解析セミナー
  • Place of Presentation: 大阪大学
  • Year and Date: 2011-12-26
• [Presentation] 双線形フーリエマルチプライヤーが有界作用素になるための滑らかさについて (2011)
  • Author(s): 冨田直人
  • Organizer: 熊本大学応用解析セミナー
  • Place of Presentation: 熊本大学
  • Year and Date: 2011-11-19
• [Presentation] 双線形フーリエマルチプライヤーに対するシャープな評価について (2011)
  • Author(s): 冨田直人
  • Organizer: 月曜解析セミナー
  • Place of Presentation: 北海道大学
  • Year and Date: 2011-11-07
• [Presentation] 双線形フーリエマルチプライヤーについて (2011)
  • Author(s): 冨田直人
  • Organizer: 三大学偏微分方程式セミナー
  • Place of Presentation: 中央大学
  • Year and Date: 2011-10-26
• [Presentation] On the L^p-boundedness of pseudo-differential operators with symbols of limited smoothness (2011)
  • Author(s): N. Tomita
  • Organizer: ISAAC Congress 2011
  • Place of Presentation: Peoples' Friendship University of Russia(Russia, Moscow)
  • Year and Date: 2011-08-24
• [Presentation] On the L^p-boundedness of pseudo-differential operators with symbols of limited smoothness (2011)
  • Author(s): N.Tomita
  • Organizer: ISAAC Congress 2011
  • Place of Presentation: Peoples' Friendship University of Russia, Russia
  • Year and Date: 2011-08-24
• [Presentation] Sharp estimates for bilinear Fourier multipliers (2011)
  • Author(s): N. Tomita
  • Organizer: 調和解析と非線形偏微分方程式
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2011-07-04
• [Presentation] 双線形フーリエマルチプライヤーに対するH￥" ormander型の定理について (2011)
  • Author(s): 冨田直人
  • Organizer: 数理科学セミナー
  • Place of Presentation: 茨城大学
  • Year and Date: 2011-03-09
• [Presentation] 多重線形フーリエマルチプライヤーに対するHormander型の定理について (2011)
  • Author(s): 冨田直人
  • Organizer: 神戸解析セミナー
  • Place of Presentation: 神戸大学
  • Year and Date: 2011-02-01
• [Presentation] 多重線形フーリエマルチプライヤーが有界作用素になるための滑らかさについて (2010)
  • Author(s): 冨田直人
  • Organizer: 調和解析セミナー
  • Place of Presentation: 日本大学
  • Year and Date: 2010-12-25
• [Presentation] A Hormander type multiplier theorem for multilinear operators (2010)
  • Author(s): N. Tomita
  • Organizer: Microlocal Day# 2,
  • Place of Presentation: Imperial College London(England, London)
  • Year and Date: 2010-12-03
• [Presentation] A Hormander type multiplier theorem for multilinear operators. 2 (2010)
  • Author(s): 冨田直人
  • Organizer: 実解析学シンポジウム
  • Place of Presentation: 九州工業大学
  • Year and Date: 2010-11-12
• [Presentation] 双線形フーリエマルチプライヤーが有界作用素になるための微分回数について (2010)
  • Author(s): 冨田直人
  • Organizer: 偏微分方程式の諸問題
  • Place of Presentation: 東海大学
  • Year and Date: 2010-10-31
• [Presentation] On the L^p-boundedness of pseudo-differential operators with symbols of limited smoothness (2010)
  • Author(s): N. Tomita
  • Organizer: Joint workshop on PDE at Jinhua
  • Place of Presentation: Zhejiang Normal University(China, Zhejiang)
  • Year and Date: 2010-09-28
• [Presentation] A Hormander type multiplier theorem for multilinear operators (2010)
  • Author(s): N. Tomita
  • Organizer: International Workshop" Fourier Analysis and Partial Differential Equations"
  • Place of Presentation: University of Gottingen(Germany, Gottingen)
  • Year and Date: 2010-06-14
• [Presentation] A Hormander type multiplier theorem for multilinear operators (2010)
  • Author(s): N.Tomita
  • Organizer: International Workshop "Fourier Analysis and Partial Differential Equations"
  • Place of Presentation: University of Gottingen (Germany)(招待講演)
  • Year and Date: 2010-06-14
• [Presentation] 双線形フーリエマルチプライヤーが有界作用素になるための微分回数について (2010)
  • Author(s): 冨田直人
  • Organizer: 神楽坂解析セミナー
  • Place of Presentation: 東京理科大学
  • Year and Date: 2010-01-23
• [Presentation] On the L^p-boundedness of pseudo-differential operators with non-regular symbols (2009)
  • Author(s): N. Tomita
  • Organizer: Harmonic Analysis and its Applications at Pohang 2009
  • Place of Presentation: Pohang University of Science and Technology(South Korea, Pohang)
  • Year and Date: 2009-11-26
• [Presentation] On the L^p-boundedness of pseudo-differential operators with non-regular symbols (2009)
  • Author(s): N. Tomita
  • Organizer: Harmonic Analysis and Partial Differential Equations
  • Place of Presentation: Harmonic Analysis and Partial Differential Equations
  • Year and Date: 2009-09-30
• [Presentation] Unimodular Fourier multipliers on modulation spaces (2009)
  • Author(s): N. Tomita
  • Organizer: 調和解析と非線形偏微分方程式
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2009-06-08
• [Presentation] On the L^p-boundedness of pseudo-differential operators with non-regular symbols (2009)
  • Author(s): N. Tomita
  • Organizer: Harmonic Analysis and Partial Differential Equations with Applications
  • Place of Presentation: Beijing Normal University(China, Beijing)
  • Year and Date: 2009-05-28
• [Presentation] On the L^p-boundedness of pseudo-differential operators with non-regular symbols (2009)
  • Author(s): N.Tomita
  • Organizer: Harmonic Analysis and Partial Differential Equations with Applications
  • Place of Presentation: Beijing Normal University (CHINA)
  • Year and Date: 2009-05-28