Speaker: Robert Anderson (University of Arkansas)

Title: Multiplication and Composition Operators on Sequence Besov Spaces 

Abstract: The sequence  Besov space $b_p$, $p>1$, is the space of analytic functions $f(z)=\sum_{n=0}^{\infty} a_n\, z^n$ on the open unit disk $\mathbb D$ with $$\sum_{n=0}^{\infty} n^{p-1}\, |a_n|^p<\infty\, .$$ We will give a brief introduction to the space $b_p$, as well as explore how certain operators behave on the space. For example, let $\varphi$ be an analytic self-map of $\mathbb D$. We study the multiplication operator $M_\varphi$ on $b_p$ and look at examples including when $\varphi$ is a polynomial. We also study the composition operator $C_\varphi$ on $b_p$, and in more depth on $b_2$ the Dirichlet space. The culmination will be an analogue of the Littlewood Theorem on Hardy spaces for $b_2$.

Zoom link: https://uark.zoom.us/j/87503165233?pwd=S7QdLHdFaJYEkZL3at0OV4aE2rRPwh.1