  We give explicit time lower bounds in the Lebesgue spaces for all nontrivial
solutions of nonlinear Schr\"odinger equations bounded in the energy space. The
result applies for these equations set in any domain of $\R^N,$ including the
whole space. This also holds for a large class of nonlinearities, thereby
extending the results obtained by Hayashi and Ozawa in \cite{MR91d:35035} and
by the author in \cite{beg3}.
