Applications of harmonic analysis to mathematics in general

• Project/Area Number: 24740085
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Tokyo Metropolitan University
• Principal Investigator: SAWANO Yoshihiro 首都大学東京, 理工学研究科, 准教授 (40532635)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 関数空間 / 再生核 / 積分作用素 / 国際研究者交流 / 国際情報交換 / Besov空間 / Morrey空間 / アトム分解 / 作用素の有界性 / 変動指数ルベーグ空間 / 逆写像 / バナッハ関数空間 / Triebel-Lizorkin空間 / モレー空間 / 中国 / ドイツ / カザフスタン

Outline of Final Research Achievements

We summarize what we obtained in the present research. 1. I proposed many types
of atomic decompositions in many function spaces. 2. I proved a fundamenatal theorem which was folklore. The proof can not be found elsewhere in the literature. 3. I investigated Morrey spaces and related function spaces. 4. I tried to express the Dirac delta in terms of the reproducing kernel Hilbert spaces.

Research Products

• [Journal Article] Characterizations for the generalized fractional integral operators on Morrey spaces (2014)
  • Author(s): Eridani, H. Gunawan, E. Nakai and Y. Sawano
  • Journal Title: Math. Inequal. Appl. Volume: 17-2
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] A new Brezis-Gallouet-Wainger inequality from the viewpoint of the real interpolation functors (2014)
  • Author(s): Y. Sawano
  • Journal Title: Math. Nachr. Volume: 287-3
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Approximation in Banach space by linear positive operators (2014)
  • Author(s): A. Ghorbanalizadeh and Y. Sawano
  • Journal Title: Positivity Volume: 18-3
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Fractional type Marcinkiewicz integral operators associated to surfaces (2014)
  • Author(s): Y. Sawano and K. Yabuta
  • Journal Title: J. Inequal. Appl. Volume: 232 Pages: 1-28
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Orlicz-Hardy spaces and their duals (2014)
  • Author(s): E. Nakai and Y. Sawano
  • Journal Title: Sci. China Math. Volume: 57-5
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Atomic decomposition for Morrey spaces (2014)
  • Author(s): Takeshi Iida, Yoshihiro Sawano and Hitoshi Tanaka
  • Journal Title: Zeitschrift für Analysis und ihre Anwendungen Volume: 33 Pages: 149-170
  • Peer Reviewed
• [Journal Article] Atomic decompositions of Hardy spaces with variable exponents and its application to bounded linear operators. (2013)
  • Author(s): Yoshihiro Sawano
  • Journal Title: Integral Equations and Operator Theory Volume: 77 Pages: 123-148
  • Peer Reviewed
• [Journal Article] A new framework for generalized Besov-type and Triebel-Lizorkin-type spaces. (2013)
  • Author(s): Liang, Yiyu; Yang, Dachun; Yuan, Wen; Sawano, Yoshihiro; Ullrich, Tino
  • Journal Title: Dissertationes Mathematicae Volume: 489 Pages: 1-114
  • Peer Reviewed
• [Journal Article] Sobolev Embeddings for Generalized Riesz Potentials of Functions in Morrey Spaces $L^{(1,\varphi)}(G)$ over Nondoubling Measure Spaces (2013)
  • Author(s): Yoshihiro Sawano and Tetsu Shimomura
  • Journal Title: Journal of function spaces and applications Volume: 2013 Pages: 1-12
  • Peer Reviewed
• [Journal Article] Applications of Littlewood-Paley Theory for $B^\sigma$-Morrey Spaces to the Boundedness of Integral Operators (2013)
  • Author(s): Yasuo Komori-Furuya, Katsuo Matsuoka, Eiichi Nakai, and Yoshihiro Sawano
  • Journal Title: Journal of function spaces and applications Volume: 2013 Pages: 1-21
  • Peer Reviewed
• [Journal Article] Sobolev embeddings for Riesz potentials of functions in non-doubling Morrey spaces of variable exponents (2013)
  • Author(s): Yoshihiro Sawano and Tetsu Shimomura
  • Journal Title: Collectanea Mathematica Volume: online Pages: 1-38
  • Peer Reviewed
• [Journal Article] Hardy spaces with variable exponents and generalized Campanato spaces (2012)
  • Author(s): Eiichi Nakai and Yoshihiro Sawano
  • Journal Title: Journal of functional analysis Volume: 262 Pages: 3665-3748
  • Peer Reviewed
• [Journal Article] Sharp bounds for multilinear fractional integral operators on Morrey type spaces (2012)
  • Author(s): Takeshi Iida, Enji Sato, Yoshihiro Sawano and Hitoshi Tanaka
  • Journal Title: Positivity Volume: 16 Pages: 339-358
  • Peer Reviewed
• [Presentation] いろいろな関数空間のnon-smooth atomic decompositionについて (2014)
  • Author(s): 澤野嘉宏
  • Organizer: 調和解析セミナー
  • Place of Presentation: 山形市
  • Year and Date: 2014-12-27
• [Presentation] Komloszの補題とそのMorrey空間の前双対への応用について (2014)
  • Author(s): 澤野嘉宏
  • Organizer: 実解析シンポジウム
  • Place of Presentation: 富山大学
  • Year and Date: 2014-10-31
• [Presentation] Decompositions of Morrey spaces (2014)
  • Author(s): 澤野嘉宏
  • Organizer: Xiamen大学解析セミナー
  • Place of Presentation: Xiamen大学
  • Year and Date: 2014-09-17
  • Invited
• [Presentation] Morrey spaces for non-doubling measures (2014)
  • Author(s): 澤野嘉宏
  • Organizer: Xiamen大学解析セミナー
  • Place of Presentation: Xiamen大学
  • Year and Date: 2014-09-10
  • Invited
• [Presentation] Three remarks on Morrey spaces and related function spaces (2014)
  • Author(s): 澤野嘉宏
  • Organizer: EACHAA2015
  • Place of Presentation: 牡丹江師範大学
  • Year and Date: 2014-07-16
  • Invited
• [Presentation] An introduction to Morrey spaces (2013)
  • Author(s): 澤野嘉宏
  • Organizer: ユーラシア中央大学（含 集中講義）
  • Place of Presentation: カザフスタン，アスタナ，ユーラシア中央大学
  • Invited
• [Presentation] An introduction to the theory of function spaces (2013)
  • Author(s): 澤野嘉宏
  • Organizer: 若手理工学セミナー
  • Place of Presentation: 釧路高専
  • Invited
• [Presentation] Hardy spaces with variable exponents (2012)
  • Author(s): Yoshihiro Sawano
  • Organizer: 43回イラン数学会議
  • Place of Presentation: タブリーツ大学
  • Invited
• [Presentation] An introduction to the theory of function spaces
  • Author(s): 澤野嘉宏
  • Organizer: 城崎若手新人セミナー
  • Place of Presentation: 豊岡市
  • Invited
• [Presentation] An introduction to the theory of function spaces
  • Author(s): 澤野嘉宏
  • Organizer: 福岡複素解析シンポジウム
  • Place of Presentation: 九大数理
  • Invited
• [Presentation] A history of variable Lebesgue spaces
  • Author(s): 澤野嘉宏
  • Organizer: 関数空間セミナー
  • Place of Presentation: 東京理科大
• [Book] 早わかりベクトル解析 (2014)
  • Author(s): 澤野嘉宏
  • Total Pages: 200
  • Publisher: 共立出版
• [Book] かんどころシリーズ (2014)
  • Author(s): 澤野嘉宏
  • Total Pages: 198
  • Publisher: ベクトル解析早わかり
• [Remarks] 首都大学東京理工学研究科数学専攻 澤野嘉宏のホームページ
  • URL: http://www.comp.tmu.ac.jp/yosihiro/