Gestur Ólafsson, Louisiana State University

Carlos Argaez Garcia, February 11, 2021

Math colloquium

Speaker: Gestur Ólafsson, Louisiana State University

Title: Atomic decomposition of Bergman spaces on Hermitian Symmetric Spaces

Room: Zoom link will be sent by email
Time: Tuesday 16th February, 16:00hrs

Abstract:

Hermitian symmetric spaces, bounded or unbounded, and spaces of functions or distributions on those spaces show up naturally in com- plex analysis, Lie theory, functional analysis and several other parts of mathematics. In this talk we will discuss some resent work on dis- cretization/atomic decomposition of Bergman spaces on those domains and their unbounded realization.

The story goes back to the work of Coifman and Rochberg in the 1980’s where they provided atomic decompositions for Bergman spaces on (the unbounded realization of) bounded symmetric domains as well as on the unit ball. Their atoms were build from the Bergman kernel. One of the shortcomings of their work was that their results did not readily transfer to the bounded realization of the domain except in the case of the unit ball.

By applying representation/coorbit theory we obtain a large family of new atoms, including those of Coifman and Rochberg, for Bergman spaces on bounded symmetric domains. Our approach also allows us to describe the relation between atoms for the bounded and unbounded realizations of the domain thus solving one of the issues raised by Coif- man and Rochberg. If time allows then we will list some open questions for domains of rank higher than one.