Averages and maximal averages over Product j-varieties in finite fields

Doowon Koh, Sujin Lee

We study both averaging and maximal averaging problems for Product $j$-varieties defined by ${\Pi }_j=\{x\in {\mathbb{F}}_q^d:{\prod }_{k=1}^d{x}_k=j\}$ for $j\in {\mathbb{F}}_q^{\ast },$ where $\math…