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

Pylyp Cherevan

For the paraboloid decomposition $F={\sum }_{\Theta }{F}_{\Theta }$ with $\Theta \subset |\xi |\sim \lambda$ and radius $r={\lambda }^{-2/3}$, we prove a log-free estimate $|F|{L^{6}(Qλ)}\lesssim λ^{Σ_λ} D^{Σ_{D}} \big(\sum_…