• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to project page

2002 Fiscal Year Final Research Report Summary

Harmonic Analysis for Some Orthogonal Expansions

Research Project

Project/Area Number 13640160
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionKanazawa University

Principal Investigator

KANJIN Yuichi  Kanazawa University, Faculty of Engineering, Professor, 工学部, 教授 (50091674)

Co-Investigator(Kenkyū-buntansha) SATO Shuichi  Kanazawa University, Faculty of Education, Associate Professor, 教育学部, 助教授 (20162430)
ICHINOSE Takasi  Kanazawa University, Faculty of Science, Professor, 理学部, 教授 (20024044)
TSUCHIYA Masaaki  Kanazawa University, Faculty of Engineering, Professor, 工学部, 教授 (50016101)
TOHGE Kazuya  Kanazawa University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (30260558)
Project Period (FY) 2001 – 2002
KeywordsHardy space / Paley's inequality / Hausdorff operator / diffusion equation / the self-adjoint Trotter-Kato product formula / Marcinkiewicz integral / Riccati differential equation
Research Abstract

Our research results are summarized as follows. The head investigator Kanjin has obtained Paley's inequality and Hardy's inequality with respect to the Jacobi expansions. The classical Peley's inequality and Hardy's inequality are two of the most familiar inequalities on the Fourier coefficients of functions in the Hardy space of certain analytic functions in the unit disc. The inequalities were originally proved by complex method. It is difficult to study orthogonal expansions by using complex method. Recent development of the real Hardy space theory, especially the atomic decomposition characterization or the real Hardy space and BMO space duality, allows to discuss problems on inequalities with respect to orthogonal expansions. Our Hardy's inequality have proved by applying the atomic decomposition to the Jacobi function system and Our Paley's inequality has gotten by using the real Hardy space and BMO space duality. Further, he has studied the Cesaro operator and, generally, the Hausdorff operator. The result says that the Hausdorff operator is bounded on the real Hardy space with parameter p smaller than one under some conditions.
The investigator Tsuchiya has investigated convergence of Dirichlet forms of diffusion process without assuming that the underlying measures are fixed or compatible with a fixed one. Ichinose has obtained more results on the self-adjoint Trotter-Kate product formula with operator norm. Sato has considered Marcinkiewicz integrals arising from rough kernels satisfying LlogL condition on the unit (n-l)-sphere and proved the weak type (1,1) estimates. Tohge has studied a Riccati differential equation whose coefficient is expressible in terms of a special Weierstrass pe-function and shown that all the solutions are meromorphic.

  • Research Products

    (18 results)

All Other

All Publications (18 results)

  • [Publications] Y.Kanjin: "The Hausdorff operators on the real Hardy spaces H^P(R)"Studia Math.. 148. 37-45 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.Kanjin: "Paley's inequality for the Jacobi expansions"Bull.London Math.Soc.. 33. 483-491 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 勘甚裕一: "直交関数系の調和解析"数学(岩波書店). 55. 55-71 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.Ogura: "Convergence of local type Dirichlet forms to a non-local one"Annales del insitut Herri Poincare, Probabilites et Statistiques. 38. 507-556 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] P.Exner: "Geometrically induced spectrum in curved leak wives"J.Phys.A : Math.Gen.. 34. 1439-1450 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] D.Fan: "Transferonce on certain multilinear multiplier operators"J.Austral.Math.Soc.. 70. 37-55 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y. Kanjin: "The Hausdorff operators on the real Hardy spaces HpR"Studia Math.. 148. 37-45 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y. Kanjin and K. Sato: "Paley's inequality for the Jacobi expansions Bull"London Math. Soc.. 33. 483-491 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H. Kawakami and M. Tsuchiya: "C^∞ smoothing of manifolds of fractional order and basic properties of the Whitney topology on the spaces of Holder maps"Internat. J. Appl. Math.. 6. 319-340 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y. Ogura, M. Tomisaki and M. Tsuchiya: "Convergence of local type Dirichlet forms to a non-local one, Annales de l' Institut Henri Poincare"Probabilites et Statistiques. 38. 507-556 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T. Ichinose: "Norm convergence of the Lie-Trotter-Kato product formula and imaginary-time path integral"J. Korean Math. Soc.. 38. 337-348 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] P. Exner and T. Ichinose: "Geometrically induced spectrum in curved leaky wires"J. Phys. A : Math. Gen.. 34. 1439-1450 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T. Ichinose and H. Tamura: "On the norm convergence of the self-adjoint Trotter-Kato product formula with error bound"Proc. Indian Acad. Sci. (Math. Sci.). 112. 99-106 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] D. Fan and S. Sato: "Transference on certain multilinear multiplier operators"J. Austral. Math. Soc.. 70. 37-55 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] D. Fan and S. Sato: "Weak type (1,1) estimates for Marcinkiewicz integrals with rough kernels"Tohoku Math. J.. 53. 265-284 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] C.-P. Chen, D. Fan and S. Sato: "deLeeuw's theorem on Littlewood-Paley functions"Nagoya Math. J.. 165. 23-42 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo, and K. Tohge: "Complex difference equations of Malmquist type"Computational Methods and Function Theory. 1. 27-39 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K. Ishizaki, I. Laine, S. Shimomura and K. Tohge: "Riccati differential equations with elliptic coefficients, II"Tohoku Math. J.. 55. 99-108 (2003)

    • Description
      「研究成果報告書概要(欧文)」より

URL: 

Published: 2004-04-14  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi