  In this note, we prove pointwise decay in time of solutions to the 3D
energy-critical nonlinear Schr\"odinger equations assuming data in $L^1\cap
H^3$. The main ingredients are the boundness of the Schr\"odinger propagators
in Hardy space due to Miyachi \cite{Miyachi} and a fractional Leibniz rule in
the Hardy space. We also extend the fractional chain rule to the Hardy space.

Analysis of PDEs;Classical Analysis and ODEs