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Research on Fourier integrals of several variables

Research Project

Project/Area Number 11640158
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

SATO Shuichi  Kanazawa Univ. Faculty of Education, associate professor, 教育学部, 助教授 (20162430)

Co-Investigator(Kenkyū-buntansha) KANJIN Yuichi  Kanazawa Univ. Faculty of Faculty of Engineering, professor, 工学部, 教授 (50091674)
Project Period (FY) 1999 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 2000: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1999: ¥900,000 (Direct Cost: ¥900,000)
KeywordsLittlewood-Paley function / rough operators / transference / multilinear operator / orthogonal series / singular integral / Marcinkiewicz function / vough operator / weak type estimate / multilinear oprator
Research Abstract

(1) We proved the weak type (1,1) estimates for the Marcinkiewicz integrals by assuming for the kernel the L log L condition on the unit sphere S^<n-1>.
(2) We proved the A_1-weighted weak (1,1) estimates for the oscillatory singular integrals of polynomial phase arising from the smooth kernels.
(3) We proved the weighted weak (1,1) estimate for the oscillatory singular integrals of polynomial phase with the rough kernels satisfying certain Dini conditions, assuming for the weights the conditions corresponding to the Dini conditions.
(4) We proved transference theorems between the multilinear multiplier operators on the Euclid space R^n and the ones on the torus T^n. Also we obtained some applications of these results.
(5) We proved transference theorems for the L^P, the weak L^P and H^P-L^P estimates between the Littlewood-Paley functions on the Euclid space R^n and those on the torus T^n. Also we obtained some applications of these results.
(6) We proved the L^P estimates for the Littlewood-Paley functions along curves and the related singular integrals, both arising from the rough kernels. As applications, we proved the L^P estimates for the Marcinkiewicz integrals along curves and the singular integrals associated to the surfaces of revolutions, both with H^1 kernels.

Report

(3 results)
  • 2000 Annual Research Report   Final Research Report Summary
  • 1999 Annual Research Report
  • Research Products

    (24 results)

All Other

All Publications (24 results)

  • [Publications] Shuichi Sato: "Weighted weak type (1,1) estimates for oscillatory singular integrals"Studia Math.. 141. 1-24 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Shuichi Sato: "Weak (1,1) estimates for Littlewood-Paley functions with rough kernels"Proceedings of the second congress ISAAC, Kluwer Academic Publishers. vol.1. 83-87 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] D.Fan and S.Sato : "Transference on certain multilinear multiplier operators"J.Austral.Math.Soc.(Ser.A). (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] D.Fan and S.Sato : "Weak type (1,1) estimates for Marcinkiewicz integrals with rough kernels"Tohoku Math.J.. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] C.-P.Chen,D.Fan and S.Sato: "de Leeuw's theorem on Littlewood-Paley functions"Nagoya Math.J.. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Shuichi Sato: "Weighted weak type (1,1) estimates for oscillatory singular integrals"Studia Math.. 141. 1-24 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] S.Sato: "Weighted weak type (1,1) estimates for oscillatory singular integrals with Dini kernels"Bull.Fac.Ed.Kanazawa Univ.Natur.Sci.. 49. 1-22 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Shuichi Sato: "Weak (1,1) estimates for Littlewood-Paley functions with rough kernels"Proceedings of the Second Congress ISAAC, Vol.1,83-87, Kluwer Academic Publishers B.V.Netherland-U.S.A.. (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Dashan Fan and Shuichi Sato: "Transference on certain multilinear multiplier operators"J.Austral.Math.Soc.(Ser.A). (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Dashan Fan and Shuichi Sato: "Weak type (1,1) estimates for Marcinkiewicz integrals with rough kernels"Tohoku Math.J.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Chang-Pao Chen, Dashan Fan and Shuichi Sato: "de Leeuw's theorem on Littlewood-Paley functions"Nagoya Math.J. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Dashan Fan and Shuichi Sato: "Remarks on Littlewood-Paley functions and singular in tegrals"(preprint).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Yuichi Kanjin: "On Hardy-type inequalities and Hankel transforms"Monatsh.Math.. 127. 311-319 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Yuichi Kanjin and Makoto Satake: "Inequalities for discrete Hardy spaces"Acta Math.Hungar.. 89. 301-313 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Yuichi Kanjin and Kunio Sato: "Paley's inequality for the Jacobi expansions"Bull.London Math.Soc.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Yuichi Kanjin: "The Hausdorff operators on the real Hardy spaces Hp (R)"(preprint).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Shuichi Sato: "Weighted weak type (1,1) estimates for oscillatory singular integrals"Studia Math.. 141. 1-24 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Shuichi Sato: "Weak (1,1) estimates for Littlewood-Paley functions with rough kernels"Proceedings of the second congress ISAAC, Kluwer Academic Publishers. vol.1. 83-87 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Dashan Fan and Shuichi Sato: "Transference on certain multilinear multiplier operators"J.Austral.Math.Soc.(Ser.A). (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] Dashan Fan and Shuichi Sato: "Weak type (1,1) estimates for Marcinkiewicz integrals with rough kernels"Tohoku Math.J.. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] Chang-Pao Chem,Dashan Fan and Shuichi Sato: "de Leeuw's theorem on Littlewood-Paley functions "Nagoya Math.J. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] Shuichi Sato: "Weak (1,1) estimates for Littlewood-Paley functions with rough kernels"Proceedings of the Second Congress ISAAC, Kluwer Academic Pub..

    • Related Report
      1999 Annual Research Report
  • [Publications] Shuichi Sato: "Weighted weak type (1,1) estimates for oscillatory singular integrals"Studia Math..

    • Related Report
      1999 Annual Research Report
  • [Publications] Shuichi Sato: "Weighted weak type (1,1) estimates for oscillatory singular integrals With D_<ini> kernels"Bull. Fac. Ed. Kanazawa Univ. Natur. Sci.. 49. 1-22 (2000)

    • Related Report
      1999 Annual Research Report

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Published: 1999-04-01   Modified: 2016-04-21  

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