## \ell^p improving and sparse inequalities for averages along the square integers

Series
Analysis Seminar
Time
Wednesday, September 11, 2019 - 1:55pm for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Rui Han – Georgia Tech
Organizer

Let $f$ be defined on $\mathbb{Z}$. Let $A_N f$ be the average of $f$ along the square integers.

We show that $A_N$ satisfies a local scale-free $\ell^{p}$-improving estimate, for $3/2 This parameter range is sharp up to the endpoint. We will also talk about sparse bounds for the maximal function$A f =\sup _{N\geq 1} |A_Nf|\$. This work is based on a joint work with Michael T. Lacey and Fan Yang.