Study of singular integrals associated to surfaces

• Project/Area Number: 23540228
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kwansei Gakuin University
• Principal Investigator: YABUTA KOZO 関西学院大学, 数理科学研究センター, 客員研究員 (30004435)
• Co-Investigator(Kenkyū-buntansha): KITAHARA KAZUAKI 関西学院大学, 理工学部, 教授 (40195277)
• Co-Investigator(Renkei-kenkyūsha): SATO SHUUICHI 金沢大学, 人間社会研究域学校教育系, 准教授 (20162430)
• Project Period (FY): 2011-04-28 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000); Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: 調和解析 / フーリエ解析 / 実解析 / 函数解析 / 実函数論 / 函数解析学 / 特異積分 / 関数解析学 / 解析学 / 近似論

Outline of Final Research Achievements

For singular integrals with kernel associated to the surface of the form {x=Ψ(|y|)} etc, we obtained several good estimates not only in Lp but also in Triebel-Lizorkin spaces.
we published 14 results for singular integrals with rough kernel, vector space valued singular integrals and multilinear singular integrals. These contribute to the development of the study of singular integrals.

Research Products

• [Journal Article] Littlewood-Paley functions on homogeneous groups (2016)
  • Author(s): Yong DING, Shuichi SATO
  • Journal Title: Forum Math. Volume: 28 Issue: 1 Pages: 43-55
  • DOI: 10.1515/forum-2014-0058
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Remark on the Triebel-Lizorkin space boundedness of singular integrals associated to surfaces (2015)
  • Author(s): Kozo YABUTA
  • Journal Title: Scientiae Mathematicae Japonicae Volume: 28 Pages: 10-10
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Triebel-Lizorkin space boundedness of rough singular integrals associated to surfaces (2015)
  • Author(s): Kozo YABUTA
  • Journal Title: Journal of Inequalities and Applications Volume: 2015:107 Issue: 1
  • DOI: 10.1186/s13660-015-0630-7
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] On multilinear Littlewood-Paley operators (2015)
  • Author(s): Xi CHEN, Qingying XUE, Kozo YABUTA
  • Journal Title: Nonlinear Analysis Volume: 115 Pages: 25-40
  • DOI: 10.1016/j.na.2014.12.001
  • NAID: 120002907447
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Remarks on a subspace of Morrey spaces (2014)
  • Author(s): Takashi IZUMI, Enji SATO, Kozo YABUTA
  • Journal Title: Tokyo Journal of Mathematics Volume: 37 Issue: 1 Pages: 185-197
  • DOI: 10.3836/tjm/1406552438
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Fractional type Marcinkiewicz integral operators associated to surfaces (2014)
  • Author(s): Yoshihiro SAWANO, Kozo YABUTA
  • Journal Title: Journal of Inequalities and Applications. Volume: 2014:232 Issue: 1
  • DOI: 10.1186/1029-242x-2014-232
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Boundedness of singular integrals associated to surfaces of revolution on Triebel-Lizorkin spaces (2014)
  • Author(s): Wenjuan LI, Zengyan SI, Kozo YABUTA
  • Journal Title: Forum Mathematicum Volume: - Issue: 1 Pages: 57-75
  • DOI: 10.1515/forum-2014-0066
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] A Note on Two Point Taylor Expansion III (2014)
  • Author(s): Kazuaki KITAHARA，T OKUNO
  • Journal Title: International Journal of Modeling and Optimization Volume: 4 Issue: 4 Pages: 287-291
  • DOI: 10.7763/ijmo.2014.v4.387
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] On the boundedness of multilinear Littlewood-Paley g_λ^* function (2014)
  • Author(s): Shaoguang SHI, Qingying XUE and Kozo YABUTA
  • Journal Title: J. Math. Pures Appl. (9) Volume: 101 Issue: 3 Pages: 394-413
  • DOI: 10.1016/j.matpur.2013.06.007
  • Peer Reviewed
• [Journal Article] Fractional type Marcinkiewicz integral operators on function spaces (2014)
  • Author(s): Qingying XUE, Kozo YABUTA and Jingquan YAN
  • Journal Title: Forum Mathematicum Volume: 未定 Issue: 5 Pages: 3079-3109
  • DOI: 10.1515/forum-2013-0200
  • Peer Reviewed
• [Journal Article] On the Boundedness of Fractional type Marcinkiewicz Integral Operators (2014)
  • Author(s): Qingying XUE, Kozo YABUTA and Jingquan YAN
  • Journal Title: Mathematical Inequalities & Applications Volume: 未定
  • Peer Reviewed
• [Journal Article] Remarks on L2 boundedness of Littlewood-Paley operators. (2013)
  • Author(s): Kozo YABUTA
  • Journal Title: Analysis (Berlin) Volume: 33 Issue: 3 Pages: 209-218
  • DOI: 10.1524/anly.2013.1144
  • Peer Reviewed
• [Journal Article] On a number theoretic problem by Blanc (2013)
  • Author(s): K. Kitahara, T. Shimotomai and S. Nagata
  • Journal Title: Scientiae Mathematicae Japonicae Volume: 76 Pages: 281-288
  • NAID: 10031187818
  • Peer Reviewed
• [Journal Article] A visit to the weak elementary Euclidean Pasch free geometry (2013)
  • Author(s): C. Omoto and K. Kitahara
  • Journal Title: Scientiae Mathematicae Japonicae Volume: 76 Pages: 367-374
  • NAID: 10031187825
  • Peer Reviewed
• [Journal Article] Weighted version of Carleson measure and multilinear Fourier multiplier (2013)
  • Author(s): Kozo YABUTA, Wenjuan LI
  • Journal Title: Forum Mathematicum
  • Peer Reviewed
• [Journal Article] Rough singular integrals associated to submanifolds (2012)
  • Author(s): Kozo YABUTA, Wenjuan LI
  • Journal Title: Taiwanese Journal of Mathematics Volume: 16 Pages: 1557-1587
  • Peer Reviewed
• [Journal Article] Some remarks on Marcinkiewicz integrals along submanifolds (2012)
  • Author(s): Kozo YABUTA, Wenjuan LI
  • Journal Title: Taiwanese Journal of Mathematics Volume: 16 Pages: 1647-1679
  • Peer Reviewed
• [Journal Article] A remark to the $L^2$L2 boundedness of parametric Marcinkiewicz integral (2012)
  • Author(s): Kozo YABUTA, Yong DING
  • Journal Title: Jounal of Mathematical Analysis and Applications Volume: 387 Issue: 2 Pages: 691-697
  • DOI: 10.1016/j.jmaa.2011.09.020
  • Peer Reviewed
• [Presentation] Triebel-Lizorkin space boundedness of Marcinkiewicz integrals associated to surfaces (2015)
  • Author(s): Kozo YABUTA
  • Organizer: The International Conference on Harmonic Analysis and Applications
  • Place of Presentation: Central China Normal University, Wuhan, P.R. China
  • Year and Date: 2015-05-22
  • Int'l Joint Research / Invited
• [Presentation] Weighted estimates for fractional type Marcinkiewicz integral operators associated to surfaces (2014)
  • Author(s): Kozo YABUTA
  • Organizer: International Conference on Harmonic Analysis and Applications .
  • Place of Presentation: Chern Institute of Mathematics, Nankai University, Tianjin, China
  • Year and Date: 2014-06-10 – 2014-06-14
  • Invited
• [Presentation] Fractional type Marcinkiewicz integral operators on function spaces (2012)
  • Author(s): Kozo YABUTA
  • Organizer: Harmonic Analysis and Its applications
  • Place of Presentation: Zhejiang Normal University(China)
  • Invited
• [Book] Some Topics in Harmonic Analysis and Applications, ALM (Advanced Lectures in Mathematics), vol 34 (2015)
  • Author(s): Y. Sawano and K. Yabuta, W. Beckner, D-C. Chen, D. Yang and S. Yang, J. Yang, D. Fan and M. Wang, C. Miao, G. Xu and L. Zhao, A. Miyachi and N. Tomita, Z. Shen, C. Sogge and S. Zelditch, A. Volberg, J. Xiao and Z. Zhai (Editors:J. Li, X. Li and G. Lu)
  • Total Pages: 422
  • Publisher: Higher Education Press, Beijing, P. R. China and International Press, Somerville, MA, U.S.A.