Date of Graduation
5-2026
Document Type
Thesis
Degree Name
Bachelor of Science in Mathematics
Degree Level
Undergraduate
Department
Mathematical Sciences
Advisor/Mentor
Maria Tjani
Committee Member
Gennady Uraltsev
Second Committee Member
Paolo Mantero
Third Committee Member
Benjamin Pierce
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 $b_2$.
Keywords
Analysis, Sequence, Besov, Operator, Composition, Multiplication
Citation
Anderson, R. (2026). Bounded Multiplication and Composition Operators on Sequence Besov Spaces. Mathematical Sciences Undergraduate Honors Theses Retrieved from https://scholarworks.uark.edu/mascuht/12
