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

Pointwise Decay of solutions to the energy critical nonlinear Schr\"odinger equations