Wellposedness for semirelativistic Schrödinger equation with power-type nonlinearity

In this paper, we employ Bourgain type norm to investigate the wellposedness for the Cauchy problem of one dimensional semirelativistic Schrödinger equation with cubic nonlinearity in space Hs. We extend the previous existence result to the space regularity s≥1∕4. Moreover, we point out the persistence of the solution in different regularity space is uniform by an iterate argument. Additionally, we are also able to say more for semirelativistic Schrödinger equation with general power-type nonlinearity.