Some Mizohata-Takeuchi-type estimate for exponential sums

Xuerui Yang

Let $R^{\frac{1}{2}}$ be a large integer, and $\ddot{I}‰$ be a nonnegative weight in the $R$-ball $B_R=[0,R{]}^2$ such that $\ddot{I}‰(B_R)\le R$. For any complex sequence $\{a_n\}$, define the qu…