Title: A variant of the $\Lambda(p)$-set problem in Orlicz spaces
Speaker: Donggeun Ryou (University of Rochester)
Speaker's URL: https://people.math.rochester.edu/grads/dryou/
Abstract: When $p>2$, let $S$ be a set of integers and consider the inequality $\|{f}\|_{p} \leq C(p) \|{f}\|_{2}$ where $f(x) = \sum_{n \in S} a_n e^{2\pi i n x}$ and $C(p)$ is a constant only depends on $p$. For various sets $S$, it has been studied the range $p$ where the inequality holds for any $f$.\\
However, in the opposite direction, we can fix $p$ and think of a set $S$ which satisfies the inequality. Then, $S$ is called a $\Lambda(p)$-set. In this talk, we will introduce $\Lambda(\Phi)$-sets as generalizations of $\Lambda(p)$-sets which are defined in terms of Orlicz norms. And we will discuss some results about $\Lambda(\Phi)$-sets which extends known results about $\Lambda(p)$-sets.
