永利欢乐娱人城网页版平台介绍 - 永利欢乐娱人城

时  间

报告人

报告题目

主持人

09:00—09:50

蒋春澜

(河北师范大学)

Kaplansky's Second Test Problem for Operator Algebras

杨大春

09:55—10:45

程立新

(厦门大学)

On Klee's Convex Body Problem and Application

10:50—11:40

张阳阳

(永利欢乐娱人城网页版平台介绍)

零边界条件下的复插值

14:30—15:20

步尚全

(清华大学)

Banach空间中的各种型

杨大春

15:25—16:15

袁文

(永利欢乐娱人城网页版平台介绍)

A Framework of Besov-Triebel-Lizorkin Type Spaces Based on Ball Quasi-Banach Function Sequence Spaces

 On Klee's Convex Body Problem and Application

程立新 (厦门大学)

In 1959, Klee asked that for what Banach spaces the following hold.

1. Every convex body can be uniformly approximated by strictly convex bodies;

2. Every convex body can be uniformly approximated by (Gâteaux) smooth convex bodies; 同类内容

3. Every convex body can be uniformly approximated by strictly convex and smooth convex bodies.

This talk is divided into two parts. The first part is dedicated to solving Klee’s problem. The second one is to use the results we have obtained and some stronger versions to characterize some geometric and topological properties of Banach spaces.

(This is a joint work with Prof. Chunlan Jiang, Prof. Liping Yuan and Prof. Wuyi He.)

 Kaplansky's Second Test Problem for Operator Algebras 同类内容

蒋春澜 (河北师范大学)

This report mainly discusses Kaplansky' second test problem in von Neumann algebras and provides a partial answer.

 A Framework of Besov-Triebel-Lizorkin Type Spaces Based on Ball Quasi-Banach Function Sequence Spaces

袁文 (永利欢乐娱人城网页版平台介绍)

In this talk we introduce a new and general framework of Besov–Triebel–Lizorkin type spaces based on ball quasi-Banach function sequence spaces. Taking the spaces L^p(\ell^q) and \ell^q(L^p) as models, we define the ball quasi-Banach function sequence space E and the related space Y(E) of Schwartz distributions, which contains various Besov–Triebel–Lizorkin type spaces as special cases. Under some sharp condition on the boundedness of the discrete Peetre-type operators on the sequence spaces, we establish the ϕ-transform characterization of Y(E) in the sense of Frazier and Jawerth. As applications, we obtain various equivalent characterizations of Y(E) via smooth molecules, smooth atoms, maximal functions, Littlewood–Paley functions, and wavelets, as well as the boundedness of pseudo-differential operators and generalized Calderón–Zygmund operators on Y(E). 

 零边界条件下的复插值

张阳阳 (北京师范大学)

Kenig在CBMS专著《Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems》中系统讨论了Lipschitz区域上二阶椭圆边值问题、迹/延拓机制以及与Hardy/BMO方法相关的边界正则性理论，并在Problem 3.3.19中提出：对于有界Lipschitz 区域上的带零边界条件Sobolev空间，Calderón复插值是否给出预期的精确结果。这个问题表面上属于插值理论，实质上牵涉零边界条件在复插值下的保持性、Lipschitz 域上延拓算子的精细性质，以及边界几何与椭圆边值问题之间的兼容关系，因此是调和分析、函数空间与边界值问题交叉处极具代表性的公开问题。此报告对此问题进行系统讲解，并给出构造反例的思路。