An ε-free rank-6 decoupling estimate for the paraboloid surface

Pylyp Cherevan

For the paraboloid decomposition $F={\sum }_{\hat{I}}˜F_{\hat{I}}˜$ with $\hat{I}˜\subset |\hat{I}¾|\sim \hat{I}»$ and radius $r=\hat{I}{»}^{-2/3}$, we prove a log-free estimate $|F|{L^{6}(Qλ)}\lesssim λ^{Σ_λ} D^{Σ_{D}}…