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

Research of Besov and Triebel-Lizorkin type spaces by real analytic methods

Research Project

Project/Area Number 17K14207
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Basic analysis
Research InstitutionTokyo Metropolitan University

Principal Investigator

Noi Takahiro  東京都立大学, 理学研究科, 客員研究員 (90736555)

Project Period (FY) 2017-04-01 – 2022-03-31
Project Status Completed (Fiscal Year 2021)
Budget Amount *help
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywordsベゾフ空間 / トリーベル・リゾルキン空間 / 変動指数をもつ関数空間 / 変動指数 / ルベーグ空間 / ソボレフ空間 / 荷重 / 変動指数解析 / ウェーブレット / モレー空間 / トレース作用素 / Besov空間 / Triebel-Lizorkin空間 / 関数解析 / Morrey空間 / 関数空間 / 差分による特徴付け / Besov型関数空間 / Triebel-Lizorkin型関数空間 / 実解析学 / 調和解析学 / 函数解析
Outline of Final Research Achievements

Generalized Besov-Morrey spaces and generalized Triebel-Lizorkin-Morrey spaces can be thought of as comprehending many function spaces, such as Lebesgue spaces. For these spaces, we obtained the results of characterization by differences and the boundedness of trace operator. In addition, we obtained the results of atomic decompositions and the condition of the boundedness of trace operator, which are important tools for studying the boundedness of operators in generalized Triebel-Lizorkin-Morray spaces and generalized Bezov-Morray spaces.
We obtained the results of complex interpolation, wavelet characterization, and atomic decomposition for weighted variable exponent Lebesgue spaces and weighted variable exponent Sobolev spaces.

Academic Significance and Societal Importance of the Research Achievements

ベゾフ型関数空間およびトリーベル・リゾルキン型関数空間はいずれもパラメータを適切に調整することで,ルベーグ空間などの基本的な関数空間と同一視することができるという点で重要な研究対象となる関数空間である.本研究課題では主に,一般トリーベル・リゾルキン・モレー空間と一般ベゾフ・モレー空間に対して作用素の有界性などを調べる際に重要な道具となりえる原子分解の結果やトレース作用が有界となるための条件を得た.これらの結果はルベーグ空間などの基本的な関数空間における結果の拡張であり,多くの場面で有用となりえる結果である.

Report

(6 results)
  • 2021 Annual Research Report   Final Research Report ( PDF )
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (10 results)

All 2020 2019 2018 2017

All Journal Article (3 results) (of which Peer Reviewed: 3 results) Presentation (7 results) (of which Int'l Joint Research: 4 results,  Invited: 5 results)

  • [Journal Article] Wavelet characterization of local Muckenhoupt weighted Lebesgue spaces with variable exponent2020

    • Author(s)
      M. Izuki, T. Nogayama, T. Noi and Y. Sawano
    • Journal Title

      Nonliear Analysis

      Volume: 19 Issue: 17 Pages: 1-17

    • DOI

      10.1016/j.na.2020.111930

    • URL

      https://ocu-omu.repo.nii.ac.jp/records/2016885

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Generalized Besov-Morrey spaces and generalized Triebel-Lizorkin-Morrey spaces on domains2019

    • Author(s)
      Mitsuo Izuki, Takahiro Noi
    • Journal Title

      Mathematische Nachrichthen

      Volume: 印刷中

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Characterization of generalized Besov-Morrey spaces and generalized Triebel-Lizorkin-Morrey spaces by differences2019

    • Author(s)
      Mitsuo Izuki, Takahiro Noi
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: 印刷中

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Presentation] Weighted generalized Besov-Morrey spaces and weighted generalized Triebel-Lizorkin spaces2019

    • Author(s)
      Takahiro Noi
    • Organizer
      International Conference on Function spaces and Geometric Analysis and Their Applications
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Weighted generalized Besov-Morrey spaces and weighted generalized Triebel-Lizorkin spaces2019

    • Author(s)
      Takahiro Noi
    • Organizer
      12th ISAAC Congress
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Generalized Triebel-Lizorkin-Morrey spaces and its characterization by differences2018

    • Author(s)
      野井 貴弘
    • Organizer
      調和解析と非線形偏微分方程式
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Generalized Triebel-Lizorkin-Morrey spaces and its characterization by differences2018

    • Author(s)
      野井 貴弘
    • Organizer
      Real, Complex and Functional Analysis Seminar 2018
    • Related Report
      2018 Research-status Report
  • [Presentation] Characterization of generalized Besov Morrey spaces by ball means of differences2018

    • Author(s)
      野井 貴弘
    • Organizer
      RIMS共同研究(公開型)「関数空間の深化とその周辺」
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] A characterization of generalized Besov Morrey spaces by differences2017

    • Author(s)
      野井 貴弘
    • Organizer
      Harmonic Analysis and its Applications in Tokyo at Nihon University
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] A characterization of generalized Besov Morrey spaces by differences2017

    • Author(s)
      野井 貴弘
    • Organizer
      Nonstandard growth phenomena 2017
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research

URL: 

Published: 2017-04-28   Modified: 2023-01-30  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi