Generalized free time-dependent Schr\"odinger equation with initial data in Fourier Lebesgue spaces

Consider the solution of the free time-dependent Schr\"odinger equation with initial data f. It is shown by Sj\"ogren and Sj\"olin (1989) that there exists f in the Sobolev space H^s(R^d), s=d/2 such that tangential convergence can not be widened to convergence regions. In 2010 we obtained the corresponding results for a generalized version of the Schr\"odinger equation, where -\Delta_x is replaced by an operator \phi(D), with special conditions on \phi. In this paper we show that similar results may be obtained for initial data in Fourier Lebesgue spaces.