\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: Shahaf Nitzan

$A_N f$ 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.

Georgia Institute of Technology College of Sciences