Last updated: Apr. 27, 2005

Speakers：

Peter Greiner (University of Toronto, Canada)

Der-Chen Chang (Georgetown University, U.S.A.)

Eric Sawyer (McMaster University, Canada)

Yongsheng Han (Auburn University, U.S.A.)

Javier Duoandikoetxea (Universidad del País Vasco, SPAIN)

Zhenqiu Zhang (Nankai University, China)

Organizer：

Chin-Cheng Lin (National Central University, Taiwan)   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

    “Harmonic Analysis” is one of the most traditional and important sub-branch in Mathematics. Several research fields, e.g. PDE, probability, are required the background knowledge in the Harmonic Analysis. However, it was ignored in Taiwan for long time. The key reasons are

(1) lack of harmonic analysts;

(2) without leader to systemically design research directions.

    For such reasons, we will offer a series Harmonic Analysis courses between March and May 2005, given by the domestic visiting professor, Chin-Cheng Lin. Also, in July 2005 we submit a summer school program in Harmonic Analysis. In this program we invite six international lecturers to visit Taiwan and give some advanced courses.

    We expect that there will be more graduated students studying Harmonic Analysis in Taiwan.

--Professors Greiner and Chang will give lectures 2~4 hours on each day of June 28, 29, and

   30.

--Professors Sawyer and Han will give lectures on July 1, 4, 6, 8, and 11. (Each one presents 2

    hour lectures on each day.)

--Professors Duoandikoetxea and Zhang will give lectures on July 15, 18, 20, 22, and 25. (Each

   one presents 2 hour lectures on each day.)

--A mini-conference will be held on July 13~14. Besides the above Professors Sawyer, Han,

   Duoandikoetxea, and Zhang, we will also invite some domestic researchers to joint the

   conference.

        Program

Lecture Notes for course:  Prof. Chang   Prof. Duoandikoetxea Prof. Han    Prof. Sawyer

Subjects：

Professor Greiner:

    To be announced

Professor Chang:

    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

Professor Han:

    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

Professor Zhang:

   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