Last updated: Apr. 27, 2005

Speakers:

P. Greiner (University of Toronto, Canada )

張德健 (Georgetown University, U.S.A.)

E. Sawyer (McMaster University, Canada)

韓永生 (Auburn University, U.S.A.)

J. Duoandikoetxea (Universidad del País Vasco, SPAIN)

張震球 (中國天津，南開大學)

Organizer：

林欽誠（中央大學數學系） clin@math.ncu.edu.tw

Time：

2005 June 28 ~ July 25

Place:

Lecture Room A of National Center for Theoretical Sciences,

4th Floor, The 3rd General Building, National TsingHua University

「調和分析」是數學中很傳統且重要的一個領域，但這個領域長期以來在國內卻一直被忽略。因此我們在2005年的3 ∼ 5月在清華大學開授一系列調和分析的預備課程，由中央大學林欽誠教授主講。然後在2005年的六月底至七月底在理論中心舉辦調和分析Summer School，邀請六位國外學者來台講授更advance的課程。希望能借此開啟國內年輕學子學習這一領域的興趣，並吸引一些人投入這一個領域的研究。

…6月28、29、30日由Greiner與張德健兩位教授講課，每天講授2-4小時。

…7月1∼11日由Sawyer與韓永生兩位教授講課，授課日期為：7月1、4、6、8、 11

    日（每天上、下午，分別由其中一位教授講授2小時）。

 …7月15∼25日由Duoandikoetxea與張震球兩位教授講課，授課日期為：7月

     15、 18、20、22、25日（每天上、下午，分別由其中一位教授講授2小時）。

 …7月13、14兩日，舉行一個Mini-conference。參與者除了上述 Sawyer、

     Duoandikoetxea、韓永生、與張震球四位演講者外，也會邀請國內、外的其他

    學者共同參與。

        Program

Lecture Notes for course:   Prof. Chang      Prof. Duoandikoetxea

                                               Prof. Han         Prof. Sawyer

授課內容:

Professor Greiner:

    To be announced

張德健教授：

    1. Cauchy-Szego integral and Heisenberg groups

    2. The $\bar\partial_b$ -complex on Heisenberg groups

    3. The sub Riemannian geometry induced by the sub-Laplacian on Heisenberg groups

    4. The $\bar\partial$-Neumann on model domain

Professor Sawyer:

    1. Carleson's interpolation and corona theorems

1.1 Bounded analytic functions on the unit disk

1.2 Duality and Carleson measures

1.3 Interpolating sequences on the disk

    2. Multiplier Algebras

2.1 Unconditional basic sequences, Riesz sequences

2.2 Pick property

    3. The unit ball in higher dimensions

3.1 Besov and Dirichlet spaces on the ball

3.2 Carleson measures

3.3 Holomorphic trees

3.4 Interpolating sequences on the ball

3.5 Arveson's Hardy space

3.6 Open problems

韓永生教授：

    1. Harmonic Analysis and applications

1.1 Fourier transform and some partial differential equations
1.2 The first generation of C-Z operators and partial differential equations with constant

      coefficients
1.3 The second generations of C-Z operators and psuedo-differential operators
1.4 The third generations of C-Z operators and the T1 theorem
1.5 The boundary value problems on Lipchistz domains

    2. Littlewood-Paley theory and function spaces

    3. Harmonic Analysis on spaces of homogeneous and non-homogeneous types

Professor Duoandikoetxea:

    Weights for maximal functions and singular integrals

    1. Introduction, motivation, examples

    2. The Hardy-Littlewood maximal operator and $ A_p$ weights

    3. Structure of $ A_p$ classes: factorization and extrapolation

    4. Weights for smooth singular integrals

    5. Rough singular integrals and other operators

    6. Some applications

張震球教授：

    1. $L^2$ estimate for the non-degenerate oscillatory integral operators

    2. Oscillatory integrals related to the Fourier transform

    3. Restricted theorem and the Strichartz estimates for the Schrodinger equation

    4. Bochner-Riesz summability

    5. $L^2$ estimate for the degenerate oscillatory integral operators with the polynomial phase