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2000 Fiscal Year Final Research Report Summary

SINGULAR INTEGRALS AND REAL ANALYSIS

Research Project

Project/Area Number 10440046
Research Category

Grant-in-Aid for Scientific Research (B).

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionKWANSEI GAKUIN UNIVERSITY (1999-2000)
Nara Women's University (1998)

Principal Investigator

YABUTA Kozo  Kwansei Gakuin Univ., School of Science, Professor, 理学部, 教授 (30004435)

Co-Investigator(Kenkyū-buntansha) KANJIN Yuichi  Kanazawa University, Fuculty of Engineering, Professor, 工学部, 教授 (50091674)
MIYACHI Akihiko  Tokyo Woman's Christian University, Faculty of Cultures and Science, Professor, 文理学部, 教授 (60107696)
SAKA Koichi  Akita University, Faculty of Technology and Resorces, Professor, 工学資源学部, 教授 (20006597)
NAKAJI Takahiko  Hokkaido University, Graduate School of Science, Professor, 理学研究科, 教授 (30002174)
YONEDA Kaoru  Osaka Prefectural University, Department of Integrated Sciences, Professor, 総合科学部, 教授 (80079029)
Project Period (FY) 1998 – 2000
Keywordssingular integrals / L^p space / Hardy spaces / weighted inequalities
Research Abstract

(1) Singular integrals with Calderon-Zygmund type kernels and with rough kernels
(i) A_1 weighted weak (1,1) estimates for oscillatory singular integrals with Calderon-Zygmund kernels. A_p (p>1) case is known. We have overcomed the difficulties in the case p=1.
(ii) Let Tf (x) = ∫K (x, y) f (y) dy. It is known that T is bounded from the Hardy space H^p to the local Hardy space h^p, under the condition T1 = 0. We could show that under more weak condition, Lipscitz condition, the same result holds. A counterexample was given in the critical index case.
(2) Vector valued singular integrals and Littlewood-Paley theory
New results on the boundedness of parametrized Marcinkiewicz integrals in L^p, Lipschitz, and Campanato spaces, which correspond to Littlewood-Paley's g-functions, g^*_λ-functions and Lusin's area integral. Using this and a recent result on multilinear Calderon- Zygmund singular integrals, we have an interesting result on multilinearized Littlewood-Paley operators.
(3) Fractional integrals.
We have generalized the notion of fractional integrals and studied those properties in several function spaces, such as L^p, BMO, Lipschitz, Campanato, and Morrey spaces, Orlicz spaces.
(4) Singlular integrals and Hardy spaces of discrete type.
We have molecular characterization of discrete Hardy space, and using this, we have given a theorem of fractional integrals and multiplier theorem of Marcinkiewicz type. Also, generalized discrete Hilbert transform were formulated and its weak l^1 boundedness were given.
(5) Almost everywhere convergence results.
New function space, modular function space, were introduced, and its effectiveness were studied

  • Research Products

    (14 results)

All Other

All Publications (14 results)

  • [Publications] 佐藤秀一: "Weighted weale type (1,1)estimateo for oscillatory singular integrals"Studia Mathematica. 141. 1-24 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 小森康雄: "Calderon-Zygmund Operatoro on H^P(R^n)"Scientiae Math.Japonicae. 53. 35-44 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 阪本美奈子,薮田公三: "Boundedness of Mareinlriearicz functions"Studis Mathematica. 135. 103-142 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 佐藤秀一: "Remarks on square functions in the Liti learood-Paley theory"Bull. Austral.Math.Soc.. 58. 199-211 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 中井英一: "On generalized fractional integrals"Taiwanese J.Math.. 5(発刊予定). (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 勘甚裕一,佐竹誠: "Inequalities for discrete Hardy spaces"Acta Math.Hungar.. 89. 301-313 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [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
  • [Publications] Yasuo Komori: "Calderon-Zygmund Operators on H^p (R^n)"Scientiae Mathematicae Japonicae. 53, No, 1. 35-44 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Minako Sakamoto and Kozo Yabuta: "Boundedness of Marcinkiewicz functions"Studia Math.. 135. 103-142 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Shuichi Sato: "Remarks on square functions in the Littlewood-Paley theory"Bull.Austral.Math.Soc.. 58. 199-211 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Eiichi Nakai: "On generalized fractional integrals"Taiwanese J.Math.. Vol.5 (to appear). (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [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
  • [Publications] Yasuo Komori: "Weak l^1 estimates for the generalized discrete Hilbert transforms"Far East J.Math.Sci.. (to appear). (2001)

    • Description
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  • [Publications] H.Kita, T.Miyamoto and K.Yoneda: "Modular function spaces and control functions of almost everywhere convergence"Commentation Math.. (to appear).

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

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Published: 2002-03-26  

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