$$\Lambda(p)$$-sets and their variants

Donggeun Ryou

Friday, November 19th, 2021
5:00 PM - 6:00 PM
Hylan 1106A and zoom id 270 486 5404

When $$p>2$$, let $$S$$ be a set of integers and consider the inequality $$\|f\|_{L^p(\mathbb{T})} \leq C(p) \|f\|_{L^2(\mathbb{T})}$$ where $$f(x) = \sum_{n \in S} a_n e^{2\pi i n x}$$ and $$C(p)$$ is a constant 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. This is called a $$\Lambda(p)$$-set. In this talk we discuss properties of $$\Lambda(p)$$-sets and the $$\Lambda(p)$$-set problem. We will also discuss variants of $$\Lambda(p)$$-sets which is defined in terms of Orlicz norms.

Event contact: dryou at ur dot rochester dot edu