Multi-linear forms, graphs, and $L^p$-improving measures in ${\mathbb{F}}_q^d$

Pablo Bhowmick, Alex Iosevich, Doowon Koh +1

The purpose of this paper is to introduce and study the following graph theoretic paradigm. Let $$T_{K}f(x)=\int K(x,y)f(y)d\mu (y),$$ where $f:X\to \mathbb{R}$, $X$ a set, finite or…