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Researches of weighted several variable Hardy spaces

Research Project

Project/Area Number 20540148
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

NAKAZI Takahiko (NAKAJI Takahiko)  北星学園大学, 経済学部, 教授 (30002174)

Project Period (FY) 2008 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
KeywordsHardy空間 / Toeplitz作用素 / 不変部分空間 / 多変数 / 重み付きToeplitz作用素 / ハーデー空間 / 重み付き / Toeplitz差要素
Research Abstract

We studied weighted several variable Hardy spaces mainly in the following three situations.
(1) prediction theory
(2) singular integral operator theory
(3) nonnegative boundary values of functions on weighted Hardy spaces.
For (1), we give the prediction errors for several typical weights in the unit disc. For (2), we estimate the essential norm of a singular integral operator using known nonweighted result. For (3), we extended one variable case to several variable case.

Report

(7 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report   Self-evaluation Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (52 results)

All 2012 2011 2010 2009 2008

All Journal Article (39 results) (of which Peer Reviewed: 17 results) Presentation (10 results) Book (3 results)

  • [Journal Article] An Argument of A Function in H_{1/2}2012

    • Author(s)
      T.Nakazi and T.Yamamoto
    • Journal Title

      Proc. Ed. Math. Soc

      Volume: 55 Pages: 507-511

    • Related Report
      2012 Final Research Report
  • [Journal Article] Weighted interpolation of weighted lp sequences and Carleson inequality2012

    • Author(s)
      T.Nakazi
    • Journal Title

      J. Math. Inequalities

      Volume: 6 Pages: 161-166

    • Related Report
      2012 Final Research Report
  • [Journal Article] Normal singular integral operaors with Cauchy kernel on L^22012

    • Author(s)
      T.Nakazi and T.Yamamoto
    • Journal Title

      Seminar on Function Spaces

      Volume: 21 Pages: 4-7

    • Related Report
      2012 Final Research Report
  • [Journal Article] Extremal problems in H^1 for continuous kernels on a bidisc2012

    • Author(s)
      T.Nakazi
    • Journal Title

      Seminar on Function Spaces

      Volume: 21 Pages: 8-11

    • Related Report
      2012 Final Research Report
  • [Journal Article] An argument of a function in H1/22012

    • Author(s)
      T.Nakazi
    • Journal Title

      Proc.Edinburgh Math.Soc

      Volume: 55 Pages: 507-511

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Weighted interpolation of weighted lp sequences and Carleson inequality2012

    • Author(s)
      T.Nakazi
    • Journal Title

      J.Math.Inequalities

      Volume: 6 Pages: 161-166

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Representations of functions in the Nevannlinna class2012

    • Author(s)
      T.Nakazi
    • Journal Title

      Intenational J.of Math.Analysis

      Volume: 6 Pages: 1457-1466

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Szego's Theorem and Uniform Algebras2011

    • Author(s)
      T.Nakazi
    • Journal Title

      Canad. Math. Bull

      Volume: 54 Pages: 338-346

    • Related Report
      2012 Final Research Report
  • [Journal Article] A corollary of Alexander's inequality2011

    • Author(s)
      T.Nakazi
    • Journal Title

      J. Math. Inequalities

      Volume: 5 Pages: 39-42

    • Related Report
      2012 Final Research Report
  • [Journal Article] Multipliers of a wandering subspace for a shift invariant subspace2011

    • Author(s)
      T.Nakazi
    • Journal Title

      J. Math. Anal. Appl

      Volume: 377 Pages: 251-252

    • Related Report
      2012 Final Research Report
  • [Journal Article] Three dimentional Q-algebras2011

    • Author(s)
      T.Nakazi and T.Yamamoto
    • Journal Title

      Far East J. Math. Sci

      Volume: 52 Pages: 121-148

    • Related Report
      2012 Final Research Report
  • [Journal Article] Spectra of some singular integral operators on L^2 with Cauchy kernel2011

    • Author(s)
      T.Nakazi
    • Journal Title

      Seminar on Function Spaces

      Volume: 20 Pages: 10-13

    • Related Report
      2012 Final Research Report
  • [Journal Article] Norms and essential norms of some singular integral operators on L^2 with Cauchy kernel2011

    • Author(s)
      T.Nakazi and T.Yamamoto
    • Journal Title

      Seminar on Function Spaces

      Volume: 20 Pages: 14-19

    • Related Report
      2012 Final Research Report
  • [Journal Article] Three dimentional Q-algebras2011

    • Author(s)
      中路貴彦、山本隆範
    • Journal Title

      Far East Journal of Math.Sci.

      Volume: Vol.52 Pages: 121-148

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A corollary of Alexander's inequality2011

    • Author(s)
      中路貴彦
    • Journal Title

      J.Math.Inequalities

      Volume: Vol.5 Pages: 39-42

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Szego's theorem and uniform algebras2011

    • Author(s)
      中路貴彦
    • Journal Title

      Canadian Math.Bull. 017-4

      Pages: 1-9

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Multipliers of a wandering subspaces for a shift invariant subspaces2011

    • Author(s)
      Takahiko Nakazi
    • Journal Title

      J.Math.Anal.Appl.

      Volume: 377 Pages: 251-252

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Szego's theorem and uniform algebras2011

    • Author(s)
      Takahiko Nakazi
    • Journal Title

      Canadian Math.Bull.

      Volume: 2011-017-4 Pages: 1-9

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Norms and Essencial Norms of The Singular Integral Operator with Cauthy Kernel on Weighted Lebesgue Spaces2010

    • Author(s)
      T.Nakazi and T. Yamamoto
    • Journal Title

      Integr. Equ. Oper. Theory

      Volume: 68 Pages: 101-113

    • Related Report
      2012 Final Research Report
  • [Journal Article] An argument of a function in H^{1/2}2010

    • Author(s)
      T.Nakazi and T.Yamamoto
    • Journal Title

      Seminar on Function Spaces

      Volume: 19 Pages: 44-48

    • Related Report
      2012 Final Research Report
  • [Journal Article] The spectra of Toeplitz operators on the bidisc2010

    • Author(s)
      T.Nakazi
    • Journal Title

      Seminar on Function Spaces

      Volume: 19 Pages: 101-105

    • Related Report
      2012 Final Research Report
  • [Journal Article] Norms and essential norms of the singular integral operator with Cauchy kernel on weighted Lebesgue spaces2010

    • Author(s)
      中路貴彦、山本隆範
    • Journal Title

      Integr.Equ.Oper.Theory 68

      Pages: 101-113

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Norms and essential norms of the singular integral operator with Cauchy kernel on weighted Lebesgue spaces2010

    • Author(s)
      Takahiko Nakazi
    • Journal Title

      Integr.Equ.Oper.Theory

      Volume: 68 Pages: 101-113

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Common invariant subspaces of two doubly commuting operators on l1xC22009

    • Author(s)
      T.Nakazi and M.Seto
    • Journal Title

      Nihonkai Math. J

      Volume: 20 Pages: 127-137

    • Related Report
      2012 Final Research Report
  • [Journal Article] Szego's theorem and uniform algebras (Application for Bergman space)2009

    • Author(s)
      T.Nakazi
    • Journal Title

      Seminar on Function Spaces

      Volume: 18 Pages: 76-80

    • Related Report
      2012 Final Research Report
  • [Journal Article] Interpolation problem for l^1 and an F-space2009

    • Author(s)
      中路貴彦
    • Journal Title

      Nihonkai Math.J. 19

      Pages: 75-83

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Integral operators on a subspace of holomorphic functions on the disc2009

    • Author(s)
      中路貴彦
    • Journal Title

      Taiwanise Math.J. 12

      Pages: 389-400

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generalized Riesz projections and Toeplitz operators2009

    • Author(s)
      中路貴彦・山本隆範
    • Journal Title

      Math.Inequal.Appl. 11

      Pages: 507-528

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Invariant Subspaces of Toeplitz Operators and Uniform Algebras2008

    • Author(s)
      T.Nakazi
    • Journal Title

      Bull. Belg. Math. Soc. Simon Stevin

      Volume: 15 Pages: 1-8

    • Related Report
      2012 Final Research Report
  • [Journal Article] Hyponormal Toeplitz Operators and Zeros of Polynomials2008

    • Author(s)
      T.Nakazi
    • Journal Title

      Proc. Amer. Math. Soc

      Volume: 136 Pages: 2425-2428

    • Related Report
      2012 Final Research Report
  • [Journal Article] Generalized Riesz projections and Toeplitz operators2008

    • Author(s)
      T.Nakazi and T.Yamamoto
    • Journal Title

      Math. Inequalities and Appl

      Volume: 11 Pages: 507-528

    • Related Report
      2012 Final Research Report
  • [Journal Article] Multipliers for a quotient Banach space and the Nevanlinna-Pick theorem2008

    • Author(s)
      T.Nakazi
    • Journal Title

      International J. of Pure and Appl. Math

      Volume: 44 Pages: 439-446

    • Related Report
      2012 Final Research Report
  • [Journal Article] Interpolation problem for l1 and an F-space2008

    • Author(s)
      T.Nakazi
    • Journal Title

      Nihonkai Math. J

      Volume: 19 Pages: 75-83

    • Related Report
      2012 Final Research Report
  • [Journal Article] Three dimensional commutative Banach algebras and Q-algebras2008

    • Author(s)
      T.Nakazi and T.Yamamoto
    • Journal Title

      Seminar on Function Spaces

      Volume: 17 Pages: 10-15

    • Related Report
      2012 Final Research Report
  • [Journal Article] Functions of the Nevanlinna class on the boundary2008

    • Author(s)
      T.Nakazi
    • Journal Title

      Seminar on Function Spaces

      Volume: 17 Pages: 73-75

    • Related Report
      2012 Final Research Report
  • [Journal Article] Invariant subspaces of Toeplitz operators and uniform algebras2008

    • Author(s)
      中路貴彦
    • Journal Title

      Bull.Belg.Math.Soc.-Simon Stevin 15

      Pages: 1-8

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Invariant subspaces of Toeplitz operators and uniform algebras2008

    • Author(s)
      中路 貴彦
    • Journal Title

      Bulletin of the Belgian Mathematical Society 15

      Pages: 1-8

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Hyponormal Toeplitz operators and zeros of polynomials2008

    • Author(s)
      中路 貴彦
    • Journal Title

      Proc. Amer. Math. Society 136

      Pages: 2425-2428

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some Fredholm Integration operators on a Hilbert space of holomorphic functions on the disc2008

    • Author(s)
      中路 貴彦
    • Journal Title

      International Math. Forum 3

      Pages: 13-16

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] Extreamal problems in H1 for continuous kernels on a bidisc2012

    • Author(s)
      T.Nakazi
    • Organizer
      第21回関数空間セミナー
    • Place of Presentation
      東京理科大
    • Related Report
      2012 Annual Research Report
  • [Presentation] Nomal singular integral operatorowith Cauchy kernel on L22012

    • Author(s)
      T.Yamamoto
    • Organizer
      第21回関数空間セミナー
    • Place of Presentation
      東京理科大
    • Related Report
      2012 Annual Research Report
  • [Presentation] Spectra of singular integral operators on L^2 with Cauthy kernel2011

    • Author(s)
      中路貴彦
    • Organizer
      Operator Theory and Its Application
    • Place of Presentation
      Daegu, Korea
    • Year and Date
      2011-08-26
    • Related Report
      2011 Annual Research Report
  • [Presentation] Hankel type operators and invariant subspaces2010

    • Author(s)
      中路貴彦
    • Organizer
      KOTAC
    • Place of Presentation
      インチョン大学
    • Year and Date
      2010-06-17
    • Related Report
      2010 Annual Research Report
  • [Presentation] Hankel type operators and invariant subspaces2010

    • Organizer
      KOTAC
    • Place of Presentation
      インチョン
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] The spectra of Toeplitz operators on the bufisc2010

    • Organizer
      第19回関数空間セミナー
    • Place of Presentation
      札幌
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Norms and essential norms of the singular intergral opertors2010

    • Organizer
      KOTAC
    • Place of Presentation
      インチョン
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Szego's theorem and uniform algebras2009

    • Organizer
      米韓合同数学会
    • Place of Presentation
      ソウル
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Szego's theorem and uniform algebras2009

    • Organizer
      第18回関数空間セミナー
    • Place of Presentation
      札幌
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Functions of the Nevanlinna class on the boundary2008

    • Author(s)
      中路 貴彦
    • Organizer
      第17回関数空間セミナー
    • Place of Presentation
      東京理科大
    • Year and Date
      2008-12-26
    • Related Report
      2008 Annual Research Report
  • [Book] 正則関数のなすヒルベルト空間2009

    • Publisher
      岩波数学叢書
    • Related Report
      2010 Self-evaluation Report
  • [Book] 岩波数学叢書 正則関数のなすヒルベルト空間2009

    • Author(s)
      中路貴彦
    • Total Pages
      252
    • Publisher
      岩波書店
    • Related Report
      2009 Annual Research Report
  • [Book] 解析学百科I 古典調和解析2008

    • Author(s)
      薮田, 中路, 佐藤, 田中, 宮地
    • Total Pages
      383
    • Publisher
      朝倉書店
    • Related Report
      2008 Annual Research Report

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Published: 2008-04-01   Modified: 2019-07-29  

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