Researches in complex analysis and harmonic analysis

复分析和调和分析研究

• 批准号: 06302008
• 负责人: MIYACHI Akihiko
• 金额: $ 1.28万
• 依托单位: Tokyo Woman's Christian University (1995)Hitotsubashi University (1994)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Co-operative Research (A)
• 财政年份: 1994
• 资助国家: 日本
• 起止时间: 1994 至 1995
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-06302008/
• 关键词: Fourier analysis; Harmonic analysis; Function spaces; Wavelet; Complex analysis; Several complex variables; Real analysis; Partial differential equations; 多変数フーリエ級数; 掛谷最大関数; 直交関数系; 局所コンパクト群; 多変数複素解析; Morrey空間; Hardy族; 多変数Bloch関数; BMO; Sze

This research project was done by the participants of the "Tyowa Kaiseki Semina" (=Harmonic Analysis Seminar) of 1994 and of 1995. This seminar has been held over 10 years, in the end of December in each year, the regular members are about 10, and the participants of each year are about 20.The following are the main results obtained in the research project. (1) Harmonic Analysis : Estimates for the Bochner-Riesz operator with the critical index (S.Sato) ; Properties of the class of Fourier multipliers (S.Igari, E.Sato, Y.Kanjin) ; Properties of the functions with nonnegative Fourier transforms (K.Tachizawa, T.Kawazoe, Y.Onoe) ; Estimates for some singular oscillating integrals and for some Littlewood-Paley type functions (S.Sato, K.Yabuta) ; Properties of several classical orthogonal systems of functions (Y.Kanjin, K.Ohashi). (2) Real Analysis : Estimates for the Kakeya maximal function (S.Igari, H.Tanaka) ; Generalization of the theory of interpolation and extrapolation (T.Sobukawa, T.Miyamoto). (3) Properties of various function spaces, boundedness of various operators in those function spaces, and their applications (A.Miyachi, T.Mizuhara, E.Nakai, J.Tateoka, T.Kitada, M.Satake). (4) Wavelet Theory : Microlocal wavelet theory and its applications (S.Moritoh) ; Wavelet theory related to the representations of semisimple Lie groups (T.Kawazoe). (5) Functions of Several Complex Variables : Characterizations of the Bloch functions, Harmonic analysis of the degenerate second order elliptic partial differential operators strongly pseudoconvex domains, Estimates for the tangential Cauchy-Riemann equation and for the Cauchy-Sego projection (H.Arai). (6) Studies of various partial differential equations by the use of the methods of harmonic analysis and real analysis (H.Arai, K.Kurata). (7) Studies on fractals (K.Saka, Y.Shiota, K.Kawamura).

该研究项目由1994年和1995年的“Tyowa Kaiseki Semina”（=谐波分析研讨会）的参与者完成。该研讨会已举办了10多年，每年12月底举行，正式成员约10人，每年参加者约20人。(1)谐波分析：具有临界指标的Bochner-Riesz算子的估计（S.Sato）;傅立叶乘法器类的性质（S.Igari，E.Sato，Y.Kanjin）;具有非负傅立叶变换的函数的性质（K.Tachizawa，T.Kawazoe，Y.Onoe）;某些奇异振荡积分和某些Littlewood-Paley型函数的估计（S.Sato，K.Yabuta）;几个经典正交函数系的性质（Y.Kanjin，K.Ohashi）。(2)真实的分析：Kakeya极大函数的估计（S.Igari，H.Tanaka）;内插和外插理论的推广（T.Sobukawa，T.Miyamoto）。(3)各种函数空间的性质，这些函数空间中各种算子的有界性及其应用（A.Miyachi，T.Mizuhara，E.Nakai，J.Tateoka，T.Kitada，M.Satake）。(4)小波理论：微局部小波理论及其应用（S.Moritoh）;与半单李群表示有关的小波理论（T.Kawazoe）。(5)函数的几个复杂的变量：特征的布洛赫功能，调和分析退化二阶椭圆偏微分算子强pseudoclave域，估计切柯西-黎曼方程和柯西-塞戈投影（H.荒井）。(6)用调和分析和真实的分析方法研究各种偏微分方程（H.Arai，K.Kurata）。(7)分形研究（坂、盐田、川村）。

项目成果

Akihiko Miyachi: "Atomic decomposition for Sobolev spaces and for the C^α_P spaces on general domains" Tsukuba Journal of Mathematics. (発表予定).

Akihiko Miyachi：“Sobolev 空间和一般域上的 C^α_P 空间的原子分解”筑波数学杂志（即将出版）。

Kozo Yabuta: "Boundedness of Littlewood-Paley operators" Mathematica Japonicae. 42(発表予定). (1995)

Kozo Yabuta：“Littlewood-Paley 算子的有界性”Mathematica Japonicae 42（待出版）。

Satoru Igari and Enji Sato: "Operating functions on Fourier multipliers" Tohoku Mathematica Journal. vol.46. 357-366 (1994)

Satoru Igari 和 Enji Sato：“傅里叶乘数的运算函数”东北数学杂志。

Hitoshi Arai: "Degenerate elliptic operators,Hardy spaces and diffusions on strongly pseudoconvex domains" To^^<^>hoku Math.J.46. 469-498 (1994)

Hitoshi Arai：“退化椭圆算子、强伪凸域上的 Hardy 空间和扩散”To^^<^>hoku Math.J.46。

Akihiko Miyachi: "Multiplication and factorization of fuctions in Sobolev spaces and in C^α_P spaces on general domains" Mathematische Nachrichten. 176. 209-242 (1995)

Akihiko Miyachi：“一般域上 Sobolev 空间和 C^α_P 空间中函数的乘法和因式分解” Mathematicsche Nachrichten 176. 209-242 (1995)。