On decay of the solutions for the dispersion generalized Benjamin--Ono and Benjamin--Ono equations

. We show that uniqueness results of the kind those obtained for KdV and Schr¨odinger equations ([7], [28]), are not valid for the dispersion generalized-Benjamin-Ono equation in the weighted Sobolev spaces for appropriated s and r . In particular, we obtain that the uniqueness result proved for the dispersion generalized- Benjamin-Ono equation ([13]), is not true for all pairs of solutions u 1 6 = 0 and u 2 6 = 0. To achieve these results we employ the techniques present in our recent work [6]. We also improve some Theorems established for the dispersion generalized-Benjamin-Ono equation and for the Benjamin-Ono equation ([13], [12]).