A variant of the $\Lambda(p)$-set problem in Orlicz spaces

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Analysis and Operator Theory Seminar
December 7, 2021
2:00PM - 2:50PM
Location
Zoom (please ask for the link)

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Add to Calendar 2021-12-07 14:00:00 2021-12-07 14:50:00 A variant of the $\Lambda(p)$-set problem in Orlicz spaces 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. Zoom (please ask for the link) Department of Mathematics math@osu.edu America/New_York public
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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.

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