2012春季学期：调和分析基础
| 授课教师 | 郝成春，邮箱地址 : hcc [at] amss.ac.cn |
| 课程内容 |
Chapter 1 The Fourier Transform and Tempered Distributions The $L^1$ theory of the Fourier transform The $L^2$ theory and the Plancherel theorem Schwartz spaces The class of tempered distributions Characterization of operators commuting with translations Chapter 2 Interpolation of Operators Riesz-Thorin's and Stein’s interpolation theorems The distribution function and weak $L^p$ spaces The decreasing rearrangement and Lorentz spaces Marcinkiewicz’ interpolation theorem Chapter 3 The Maximal Function and Calderón-Zygmund Decomposition Two covering lemmas Hardy-Littlewood maximal function Calderón-Zygmund decomposition Chapter 4 Singular Integrals Harmonic functions and Poisson equation Poisson kernel and Hilbert transform The Calderón-Zygmund theorem Truncated integrals Singular integral operators commuted with dilations The maximal singular integral operator Vector-valued analogues Chapter 5 Riesz Transforms and Spherical Harmonics The Riesz transforms Spherical harmonics and higher Riesz transforms Equivalence between two classes of transforms Chapter 6 The Littlewood-Paley $g$ -function and Multipliers The Littlewood-Paley $g$ -function Fourier multipliers on $L^p$ The partial sums operators The dyadic decomposition The Marcinkiewicz multiplier theorem Chapter 7 Sobolev and Hölder Spaces Riesz potentials and fractional integrals Bessel potentials Sobolev spaces Hölder spaces Chapter 8 Besov and Triebel-Lizorkin Spaces The dyadic decomposition: the smooth version Besov spaces and Triebel-Lizorkin spaces Embedding theorems and Gagliardo-Nirenberg inequalities Differential-difference norm on Besov spaces Chapter 9 BMO Spaces Sharp maximal functions and BMO spaces Sharp maximal theorem, interpolation between $L^p$ and BMO C-Z singular integral operator of type ($L^\infty$, BMO) |
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2024-05-21 天还没亮，要注意身体哦！ | © 2024 Chengchun Hao