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

2009 Fiscal Year Final Research Report

Harmonic analysis by real variable methods and its applications

Research Project

  • PDF
Project/Area Number 18340043
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionTokyo Woman's Christian University

Principal Investigator

MIYACHI Akihiko  Tokyo Woman's Christian University, 現代教養学部, 教授 (60107696)

Co-Investigator(Kenkyū-buntansha) KANJIN Yuichi  金沢大学, 大学院・自然科学研究科, 教授 (50091674)
KOZONO Hideo  東北大学, 大学院・理学研究科, 教授 (00195728)
SATO Shuichi  金沢大学, 教育学部, 准教授 (20162430)
SATO Enji  山形大学, 理学部, 教授 (80107177)
FURUYA Yasuo (小森 康雄)  東海大学, 沼津教養教育センター, 教授 (70234903)
TACHIZAWA Kazuya  北海道大学, 大学院・理学研究院, 准教授 (80227090)
SHINOHARA Masahiko  東京女子大学, 文理学部, 教授 (70086346)
OAKU Toshinori  東京女子大学, 文理学部, 教授 (60152039)
Co-Investigator(Renkei-kenkyūsha) OKADA Masami  首都大学東京, 大学院・理工学研究科, 教授 (00152314)
SUGIMOTO Mitsuru  名古屋大学, 大学院・多元数理科学研究科, 教授 (60196756)
TOMITA Naohito  大阪大学, 大学院・理学研究科, 講師 (10437337)
KOBAYASHI Masaharu  東京理科大学, 理学部, 助教 (30516480)
SAWANO Yoshihiro  京都大学, 理学部, 助教 (40532635)
NAKAI Eiichi  大阪教育大学, 教育学部, 教授 (60259900)
KANJIN Yuichi  金沢大学, 大学院・自然科学研究科, 教授 (50091674)
SATO Enji  山形大学, 理学部, 教授 (80107177)
Project Period (FY) 2006 – 2009
Keywords実解析 / 調和解析 / 関数空間 / 直交級数 / 特異積分 / ハーディー空間
Research Abstract

We introduced a function space on a domain of the Euclidean space and established its fundamental properties. The function space has several properties similar to the Hardy space on the whole Euclidean space introduced by Fefferman and Stein. In particular, we showed that the change of variables defined through diffeomorphisms, with certain properties, of the basic domains transforms the function space into another function space of the same kind. We used the function space to study classical orthogonal series. We investigated several other function spaces used in the field of time-frequency analysis and obtained several results concerning the operators acting in those spaces.

  • Research Products

    (38 results)

All 2010 2009 2008 2007 2006 Other

All Journal Article (18 results) (of which Peer Reviewed: 18 results) Presentation (20 results)

  • [Journal Article] Some weak-type estimates for singular integral operators on CMO spaces2010

    • Author(s)
      Yasuo Komori(古谷康雄), K. Matsuoka
    • Journal Title

      Hokkaido Mathematical Journal Vol.39(掲載確定)

    • Peer Reviewed
  • [Journal Article] Estimates for unimodular Fourier multipliers on modulation Spaces2009

    • Author(s)
      A. Miyachi, F. Nicola, S. Rivetti, A. Tabacco, N. Tomita
    • Journal Title

      Proceedings of the American Mathematical Society Vol.137

      Pages: 3869-3883

    • Peer Reviewed
  • [Journal Article] Change of variables for weighted Hardy spaces on a domain2009

    • Author(s)
      A. Miyachi
    • Journal Title

      Hokkaido Mathematical Journal Vol.38

      Pages: 519-555

    • Peer Reviewed
  • [Journal Article] Boundedness of the Hausdorff operators in Hp spaces, 0<p<12009

    • Author(s)
      Elijah Liflyand, Akihiko Miyachi
    • Journal Title

      Studia Mathematica Vol.194

      Pages: 279-292

    • Peer Reviewed
  • [Journal Article] Embedding relations between local Hardy and modulation spaces2009

    • Author(s)
      M. Kobayashi, A. Miyachi, N. Tomita
    • Journal Title

      Studia Mathematica Vol.192

      Pages: 79-96

    • Peer Reviewed
  • [Journal Article] Weighted Morrey spaces and a singular integral operator2009

    • Author(s)
      Yasuo Komori(古谷康雄), S. Shirai
    • Journal Title

      Mathematische Nachrichten Vol.282

      Pages: 219-231

    • Peer Reviewed
  • [Journal Article] Boundedness of several operators on weighted Herz spaces2009

    • Author(s)
      Y. Komori(古谷康雄)and K. Matsuoka
    • Journal Title

      Journal of Function Spaces and Applications Vol.7

      Pages: 1月12日

    • Peer Reviewed
  • [Journal Article] Calderon's commutator on Hp(Rn)2008

    • Author(s)
      Y. Komori(古谷康雄)
    • Journal Title

      Int. J. Pure. Appl. Math. Vol.47

      Pages: 225-234

    • Peer Reviewed
  • [Journal Article] The Cauchy integral operator on Hardy space2008

    • Author(s)
      Yasuo Komori (古谷康雄)
    • Journal Title

      Hokkaido Mathematical Journal Vol.37

      Pages: 389-398

    • Peer Reviewed
  • [Journal Article] Weighted estimates for maximal functions associated with Fourier multipliers2007

    • Author(s)
      Shuichi Sato
    • Journal Title

      Studia Sci. Math. Hungarica Vol.44

      Pages: 317-330

    • Peer Reviewed
  • [Journal Article] Non-regular pseudodifferential operators on the weighted Triebel-Lizorkin spaces2007

    • Author(s)
      Shuichi Sato
    • Journal Title

      Tohoku Mathematical Journal Vol.59

      Pages: 323-339

    • Peer Reviewed
  • [Journal Article] Transplantation theorem for Jacobi series in weighted Hardy spaces2006

    • Author(s)
      Akihiko Miyachi
    • Journal Title

      II, Mathematische Annalen Vol.336

      Pages: 111-153

    • Peer Reviewed
  • [Journal Article] Weighted Hardy spaces on an interval and Poisson integrals associated with ultraspherical series2006

    • Author(s)
      Akihiko Miyachi
    • Journal Title

      Journal of Functional Analysis Vol.239

      Pages: 446-496

    • Peer Reviewed
  • [Journal Article] Transplantation operators and Cesaro operators for the Hankel transform2006

    • Author(s)
      Yuichi Kanjin
    • Journal Title

      Studia Mathematic Vol.171

      Pages: 29-45

    • Peer Reviewed
  • [Journal Article] Singular and fractional integrals along variable surfaces2006

    • Author(s)
      Dashan Fan, Shuichi Sato
    • Journal Title

      Hokkaido Mathematical Journal Vol.35

      Pages: 61-85

    • Peer Reviewed
  • [Journal Article] A generalization of the Hankel transform and the Lorentz multipliers2006

    • Author(s)
      Enji Sato
    • Journal Title

      Tokyo Journal of Mathematics Vol.29

      Pages: 147-166

    • Peer Reviewed
  • [Journal Article] Factorization of functions in H1(Rn) and generalized Morrey spaces2006

    • Author(s)
      Yasuo Komori(古谷康雄), Takahiro Mizuhara
    • Journal Title

      Mathematische Nachrichten Vol.279

      Pages: 619-624

    • Peer Reviewed
  • [Journal Article] A note on weight classes of Muckenhoupt type on nondoubling measure spaces

    • Author(s)
      Yasuo Komori-Furuya(古谷康雄)
    • Journal Title

      Georgian Mathematical Journal (掲載確定)

    • Peer Reviewed
  • [Presentation] Fourier級数の慨収束についてのCarleson-Huntの定理2009

    • Author(s)
      宮地晶彦
    • Organizer
      調和解析セミナー
    • Place of Presentation
      岡山大学教育学部
    • Year and Date
      20091226-20091228
  • [Presentation] 多重特異積分入門2009

    • Author(s)
      小森康雄
    • Organizer
      調和解析セミナー2009
    • Place of Presentation
      岡山大学教育学部
    • Year and Date
      2009-12-26
  • [Presentation] 局所Hardy空間とmodulation空間の包含関係について2009

    • Author(s)
      小林政晴・宮地晶彦・冨田直人
    • Organizer
      日本数学会秋季総合分科会, 実関数論分科会
    • Place of Presentation
      阪大学
    • Year and Date
      2009-09-24
  • [Presentation] Unimodular Fourier multiplierのmodulation空間評価2009

    • Author(s)
      宮地晶彦・冨田直人
    • Organizer
      日本数学会秋季総合分科会, 実関数論分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-24
  • [Presentation] Change of variables for weighted Hardy spaces on a domain2009

    • Author(s)
      Akihiko Miyachi
    • Organizer
      International Symposium on Banach and Function Spaces 2009
    • Place of Presentation
      九州工業大学
    • Year and Date
      2009-09-14
  • [Presentation] Change of variables for weighted Hardy spaces on a domain2009

    • Author(s)
      Akihiko Miyachi
    • Organizer
      国際研究集会Harmonic Analysis and Partial Differential Equations
    • Place of Presentation
      北京師範大学
    • Year and Date
      2009-05-28
  • [Presentation] 領域上の重み付きハーディ空間の変数変換について2009

    • Author(s)
      宮地晶彦
    • Organizer
      東海大学談話会
    • Place of Presentation
      東海大学工学部
    • Year and Date
      2009-01-22
  • [Presentation] Div-curl lemmaとその周辺2008

    • Author(s)
      小森康雄(古谷康雄)
    • Organizer
      調和解析セミナー2008
    • Place of Presentation
      山形大学理学部
    • Year and Date
      2008-12-26
  • [Presentation] Bilinear operatorに関して2008

    • Author(s)
      佐藤圓治
    • Organizer
      調和解析セミナー2008
    • Place of Presentation
      山形大学理学部
    • Year and Date
      2008-12-25
  • [Presentation] シャープ最大関数とその応用2008

    • Author(s)
      宮地晶彦
    • Organizer
      大阪大学微分方程式セミナー
    • Place of Presentation
      大阪大学大学院理学研究科
    • Year and Date
      2008-11-21
  • [Presentation] Some weak estimates for singular integral operators on Herz spaces2008

    • Author(s)
      松岡勝男・小森康雄
    • Organizer
      実解析学シンポジウム2008
    • Place of Presentation
      山口大学理学部
    • Year and Date
      2008-11-08
  • [Presentation] Pseudo-differential operators on Hardy spaces2008

    • Author(s)
      Yasuo Komori (古谷康雄)
    • Organizer
      Harmonic Analysis and its Applications at Tokyo 2008
    • Place of Presentation
      首都大学東京
    • Year and Date
      2008-10-10
  • [Presentation] Time-Frequency解析, Dyadic Harmonic Analysis入門2007

    • Author(s)
      小森康雄(古谷康雄)
    • Organizer
      調和解析セミナー2007
    • Place of Presentation
      草津セミナーハウス
    • Year and Date
      2007-12-24
  • [Presentation] Paley's inequality of integral transform type2007

    • Author(s)
      Yuichi Kanjin
    • Organizer
      Harmonic Analysis and Orthogonal Systems
    • Place of Presentation
      Miraflores de La Sierra, Madrid, Spain
    • Year and Date
      2007-11-23
  • [Presentation] Lp estimates for singular Radon transforms and extrapolation2007

    • Author(s)
      佐藤秀一
    • Organizer
      Harmonic Analysis and its Applications at Sapporo 2007
    • Place of Presentation
      北海道大学理学部
    • Year and Date
      2007-09-04
  • [Presentation] 移植作用素とチェザロ作用素2007

    • Author(s)
      勘甚裕一
    • Organizer
      第46回実函数論・函数解析学合同シンポジウム
    • Place of Presentation
      九州大学西新プラザ
    • Year and Date
      2007-08-08
  • [Presentation] Wavelet characterization of weighted spaces2007

    • Author(s)
      立澤一哉
    • Organizer
      調和解析と非線形偏微分方程式研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-07-10
  • [Presentation] On the weighted Herz spaces and the boundedness for some sublinear operators2006

    • Author(s)
      松岡勝男・小森康雄
    • Organizer
      調和解析セミナー2006
    • Place of Presentation
      大阪教育大学天王寺キャンパス
    • Year and Date
      2006-12-25
  • [Presentation] Weighted Morrey spaces and maximal operator2006

    • Author(s)
      白井悟・小森康雄(古谷康雄)
    • Organizer
      日本数学会秋季総合分科会, 実関数論分科会
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2006-09-21
  • [Presentation] Weighted Hardy spaces on an interval and Jacobi series2006

    • Author(s)
      Akihiko Miyachi
    • Organizer
      Function Spaces VIII
    • Place of Presentation
      Bedlewo, Poland
    • Year and Date
      2006-07-07

URL: 

Published: 2011-06-18   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi