Internet Analysis Seminar

The topic of the Internet Analysis Seminar this year will be multi-parameter harmonic analysis. This topic is a out growth of harmonic analysis when attempting to understand the function theory associated to product domains such as the polydisc.

The topics of the lectures and seminar will first provide a quick introduction to standard harmonic analysis. The notion of standard here will refer to the the operators and geometric objects that behave well with respect to one-parameter dilations. Potential topics to be covered will provide an introduction to maximal functions, covering lemmas, Calderon-Zygmund operators, Carleson measures, the function space BMO and the real Hardy space. Additional topics will connect to paraproducts, commutators and T(1) Theorems.

After covering the basics, we will turn to the story in the multi-parameter world. Much of the story mirrors what we will have covered in the introduction to basic harmonic analysis. However, there will also be a decided difference. The differences arise because we will be interested in operators and geometric objects that behave well with respect to more general dilation groups. Again, potential topics to be covered will include maximal functions, covering lemmas, Calderon-Zygmund operators, Carleson measures, the function space BMO and the real Hardy space. Additional topics will connect to paraproducts, commutators and T(1) Theorems.