Applications to mathematics in general of harmonic analysis

• Project/Area Number: 21740104
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Kyoto University
• Principal Investigator: SAWANO Yoshihiro 京都大学, 大学院・理学研究科, 助教 (40532635)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2011: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 関数空間 / 再生核 / 分数べき積分作用素 / 変動指数 / アトム分解 / 再生核ヒルベルト空間 / 時間周波数解析 / フーリエ解析 / Sobolevの埋め込み定理 / 楕円型微分方程式 / 測度空間

Research Abstract

I worked on the following projects.
1. Multilinear estimates of fractional integral operators on Morrey spaces and its applications to PDE
2. Hardy spaces with variable exponents
3. Axiomatic analysis on Besov spaces
4. Writing a book in English on reproducing kernel Hilbert spaces.
5. Publishing a book in Japanese on Besov spaces

Research Products

• [Journal Article] Atomic decomposition for weighted Besov and Triebel-Lizorkin spaces. (2012)
  • Author(s): Mitsuo Izuki and Yoshihiro Sawano
  • Journal Title: Math.Nachr Volume: 285 Pages: 103-126
  • Peer Reviewed
• [Journal Article] Complex interpolation of Besov spaces and Triebel-Lizorkin spaces with variable exponents. (2012)
  • Author(s): Takahiro Noi and Yoshihiro Sawano
  • Volume: 387
  • Pages: 676-690
  • Peer Reviewed
• [Journal Article] Lower bound for sharp constants of Brezis-Gallouet-Wainger type inequalities in higher-order critical (2012)
  • Author(s): Kei Morii and Yoshihiro Sawano
  • Journal Title: Sobolev spaces on bounded domains. Commun Volume: 12 Pages: 1-16
  • Peer Reviewed
• [Journal Article] Complex interpolation of Besov spaces and Triebel-Lizorkin spaces with variable exponents (2012)
  • Author(s): Takahiro Noi, Yoshihiro Sawano
  • Journal Title: J.Math.Anal.Appl. Volume: 387 Pages: 676-690
  • Peer Reviewed
• [Journal Article] Hardy spaces with variable exponents and generalized Campanato spaces (2012)
  • Author(s): Eiichi Nakai, Yoshihiro Sawano
  • Journal Title: Journal of Functional Analysis Volume: 262 Issue: 9 Pages: 3665-3748
  • DOI: 10.1016/j.jfa.2012.01.004
  • Peer Reviewed
• [Journal Article] General Inhomogeneous Discrete Linear Partial Differential Equations with Constant Coefficients on the Whole Spaces (2012)
  • Author(s): Luis Castro, Saburoh Saitoh, Yoshihiro Sawano, Alberto Simoes
  • Journal Title: Complex Anal.Oper.Theory. Volume: (online) Pages: 15-15
  • Peer Reviewed
• [Journal Article] Olsen's inequality and its applications to Schrodingerons. Harmonic analysis and nonlinear partial differential equations (2011)
  • Author(s): Yoshihiro Sawano, Satoko Sugano and Hitoshi Tanaka
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: 51-80 Pages: 51-80
  • Peer Reviewed
• [Journal Article] Weighted norm inequalities for multilinear fractional operators on Morrey spaces. (2011)
  • Author(s): Takeshi Iida, Sato, Enji, Yoshihiro Sawano and Tanaka Hitoshi
  • Journal Title: Studia Math Volume: 205 Pages: 139-170
  • Peer Reviewed
• [Journal Article] Generalized fractional integral operators and fractional maximal operators in the framework of Morrey spaces (2011)
  • Author(s): Yoshihiro Sawano, Satoko Sugano and Hitoshi Tanaka
  • Journal Title: Trans. Amer Volume: 363 Pages: 6481-6503
  • NAID: 120003752109
  • Peer Reviewed
• [Journal Article] Weighted norm inequalities for multilinear fractional operators on Morrey spaces (2011)
  • Author(s): Enji Sato, Yoshihiro Sawano, H
  • Journal Title: Studia Mathematica Volume: 205 Issue: 2 Pages: 139-170
  • DOI: 10.4064/sm205-2-2
  • Peer Reviewed
• [Journal Article] Wavelet characterization of the pointwise multiplier space X r (2011)
  • Author(s): Sadek Gala, Yoshihiro Sawano
  • Journal Title: Functiones et Approximatio Volume: 43 Pages: 109-116
  • Peer Reviewed
• [Journal Article] Molecular decomposition of the modulation spaces. (2010)
  • Author(s): Masaharu Kobayashi and Yoshihiro Sawano
  • Journal Title: Osaka J Volume: 47 Pages: 1029-1053
  • NAID: 120004838004
  • Peer Reviewed
• [Journal Article] Modulation spaces with Aloc∞-weights. (2010)
  • Author(s): Yoshihiro Sawano
  • Journal Title: Cubo Volume: 12 Pages: 187-202
  • Peer Reviewed
• [Journal Article] Wavelet characterization of the pointwise multiplier space Xr (2010)
  • Author(s): Sadek Gala and Yoshihiro Sawano
  • Journal Title: Funct Approx. Comment. Math. Volume: 43 Pages: 109-116
  • Peer Reviewed
• [Journal Article] Sharp constants of Brezis-Gallouet-Wainger type inequalities with a double logarithmic term on bounded domains in Besov and Triebel-Lizorkin spaces (2010)
  • Author(s): Kei Morii, Tokushi Sato, Yoshihiro Sawano and Hidemitsu Wadade
  • Journal Title: Bound. Value Probl Volume: 38 Pages: 38-38
  • Peer Reviewed
• [Journal Article] Certain identities on derivatives of radial homogeneous and logarithmic functions (2010)
  • Author(s): Kei Morii, Tokushi Sato and Yoshihiro Sawano
  • Journal Title: Commun. Math. Anal Volume: 9 Pages: 51-66
  • Peer Reviewed
• [Journal Article] Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces on domains (2010)
  • Author(s): Yoshihiro Sawano
  • Journal Title: Math. Nachr. Volume: 283 Pages: 1456-1487
  • Peer Reviewed
• [Journal Article] Decompositions of Besov-Hausdorff and Triebel-Lizorkin-Hausdorff spaces and their applications (2010)
  • Author(s): Wen Yuan, Yoshihiro Sawano and Dachun Yang
  • Journal Title: J. Math. Anal. Appl. Volume: 369 Pages: 736-757
  • Peer Reviewed
• [Journal Article] Maximal operator for pseudodifferential operators with homogeneous symbols. (2010)
  • Author(s): Yoshihiro Sawano
  • Journal Title: Michigan Math. J Volume: 59 Pages: 119-142
  • Peer Reviewed
• [Journal Article] Singular integral inequalities and natural regularizations. (2010)
  • Author(s): Yoshihiro Sawano, Yamada, Masato and Saburou Saitoh
  • Journal Title: Math. Inequal. Appl. Volume: 13 Pages: 289-303
  • Peer Reviewed
• [Journal Article] Brezis-Gallouet-Wainger type inequality for Besov-Morrey spaces. (2010)
  • Author(s): Yoshihiro Sawano
  • Journal Title: Studia Math Volume: 196 Pages: 91-101
  • Peer Reviewed
• [Journal Article] New applications of Besov-type and Triebel-Lizorkin-type spaces. (2010)
  • Author(s): Yoshihiro Sawano, Dachun Yang and Wen Yuan
  • Journal Title: J. Math. Anal Volume: 363 Pages: 73-85
  • Peer Reviewed
• [Journal Article] The Haar wavelet characterization of weighted (2010)
  • Author(s): Mitsuo Izuki and Yoshihiro Sawano
  • Journal Title: J. Math. Anal. Appl. Volume: 362 Pages: 140-155
  • Peer Reviewed
• [Journal Article] Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces on domains (2010)
  • Author(s): 澤野嘉宏
  • Journal Title: Math.Nachr Volume: 283 Pages: 1456-1487
  • Peer Reviewed
• [Journal Article] The Haar wavelet characterization of weighted Herz spaces and greediness of the Haar wavelet basis (2010)
  • Author(s): 出来光夫, 澤野嘉宏
  • Journal Title: Journal of Mathematical Analysis and Applications 362 Pages: 140-155
  • Peer Reviewed
• [Journal Article] New applications of Besov-type and Triebel-Lizorkin-type spaces. (2010)
  • Author(s): 澤野嘉宏, Yang Dachun, Wen Yuan
  • Journal Title: Journal of Mathematical Analysis and Applications 363 Pages: 73-85
  • Peer Reviewed
• [Journal Article] Br'esis-Gallou" et-Wainger type inequality for Besov-Morrey spaces (2010)
  • Author(s): 澤野嘉宏
  • Journal Title: Studia Mathematica 196 Pages: 91-101
  • Peer Reviewed
• [Journal Article] Greedy bases in weighted modulation spaces. (2009)
  • Author(s): Mitsuo Izuki and Yoshihiro Sawano
  • Journal Title: Nonlinear Anal Volume: 71
  • Peer Reviewed
• [Journal Article] A note on Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces (2009)
  • Author(s): 澤野嘉宏
  • Journal Title: Act Mathematica Sinica 25 Pages: 1223-1242
  • Peer Reviewed
• [Journal Article] Truncation errors of the logarithmic potential operators (2009)
  • Author(s): 澤野嘉宏
  • Journal Title: Proc.A.Razmadze Math.Inst. 150 Pages: 115-119
  • Peer Reviewed
• [Journal Article] Fractional integral operators in nonhomogeneous spaces (2009)
  • Author(s): Gunawan H. 澤野嘉宏, Sihwaningrum I.
  • Journal Title: Bull.Aust.Math.Soc. 80 Pages: 324-334
  • Peer Reviewed
• [Journal Article] Wavelet bases in the weighted Besov and Triebel-Lizorkin spaces with Alocp-weights (2009)
  • Author(s): 出来光夫, 澤野嘉宏
  • Journal Title: Journal of Approximation Theory 161 Pages: 656-673
  • Peer Reviewed
• [Journal Article] Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces for non-doubling measures. (2009)
  • Author(s): 澤野嘉宏, 田中仁
  • Journal Title: Mathematische Nachrichten 282 Pages: 1788-1810
  • Peer Reviewed
• [Journal Article] Weighted Besov-Morrey spaces and Triebel-Lizorkin spaces
  • Author(s): Mitsuo Izuki, Yoshihiro Sawano and Hitoshi Tanaka
  • Journal Title: Harmonic analysis and nonlinear partial differential equations Volume: 22 Pages: 21-60
  • Peer Reviewed
• [Presentation] Morrey spaces for non-doubling measures (2011)
  • Author(s): 深野嘉宏
  • Organizer: Operators on Morrey type spaces and applications
  • Place of Presentation: Kirchehir大学
  • Year and Date: 2011-05-18
• [Presentation] New phase decomposition formula and its applications (2010)
  • Author(s): 澤野嘉宏
  • Organizer: 数学コロキウム
  • Place of Presentation: 国立中央大学(台湾)(招待)
  • Year and Date: 2010-11-01
• [Presentation] Maximal operator for pseudo-differential operators with homogeneous symbols (2010)
  • Author(s): 澤野嘉宏
  • Organizer: 京都大学臨時談話会
  • Place of Presentation: 京都大学
  • Year and Date: 2010-06-03
• [Presentation] A counter example concerning to the Fefferman -Phong inequality (2010)
  • Author(s): 澤野嘉宏, 田中仁, 菅野聡子
  • Organizer: 日本数学会実解析分科会
  • Place of Presentation: 慶応大学
  • Year and Date: 2010-03-27
• [Presentation] Fractional integral operators and Morrey spaces with small parameters (2010)
  • Author(s): 澤野嘉宏, 田中仁, 菅野聡子
  • Organizer: 日本数学会実解析分科会
  • Place of Presentation: 慶応大学
  • Year and Date: 2010-03-27
• [Presentation] Morrey spaces for non-doubling measures (2010)
  • Author(s): 澤野嘉宏
  • Organizer: Mathematics colloquim at Macqarie
  • Place of Presentation: 豪Macqauarie University
  • Year and Date: 2010-01-18
• [Presentation] Singular integral inequalities and natural regularizations (2010)
  • Author(s): 澤野嘉宏
  • Organizer: Taiwan National University(Taiwan-Japan Joint Workshop on Inverse Problems)
  • Place of Presentation: Taiwan National Universit
• [Presentation] Decompositions of Besov-Hausdorff and Triebel-Lizorkin-Hausdorff Spaces (2009)
  • Author(s): 澤野嘉宏
  • Organizer: Harmonic analysis and its application at Pohang
  • Place of Presentation: 韓国Pohang大学
  • Year and Date: 2009-11-28
• [Presentation] A note on Morrey spaces (2009)
  • Author(s): 澤野嘉宏
  • Organizer: インドネシアMalang大学研究集会
  • Place of Presentation: インドネシアMalang大学
  • Year and Date: 2009-08-15
• [Presentation] New phase decomposition formula and its applications (2009)
  • Author(s): 澤野嘉宏
  • Organizer: Harmonic analysis and partial differential equations with applications
  • Place of Presentation: 中国 北京師範大学
  • Year and Date: 2009-05-27
• [Book] ベゾフ空間論 (2011)
  • Total Pages: 440
  • Publisher: 日本評論社
• [Book] ベゾフ空間論 (2011)
  • Author(s): 澤野嘉宏
  • Total Pages: 420
  • Publisher: 日本評論社
• [Book] 複素解析の入り口 (2009)
  • Author(s): 澤野嘉宏
  • Total Pages: 10
  • Publisher: 数学書房
• [Book] エレガントな解法を求む(出題) (2009)
  • Author(s): 澤野嘉宏
  • Total Pages: 1
  • Publisher: 日本評論社
• [Book] エレガントな解放を求む(解説) (2009)
  • Author(s): 澤野嘉宏
  • Total Pages: 5
  • Publisher: 日本評論社
• [Remarks]
  • URL: http://www.comp.tmu.ac.jp/yosihiro/
• [Remarks]
  • URL: http://www.math.kyoto-u.ac.jp/~yosihiro/
• [Remarks]
  • URL: http://www.math.kyoto-u.ac.jp/~yosihiro/paper/paper-sawano.html