Smoothing effects of dispersive pseudodifferential equations

We discuss smoothing effects of dispersive-type pseudodifferential equations whose principal part is not necessarily elliptic. For equations with constant coefficients, a restriction theorem and a smoothing estimate of the resolvent of the principal part obtain smoothing estimates of solutions in weighted Lebesgue spaces. Moreover, we discuss well-posedness of the initial value problem and an alternative approach to the smoothing effects of general dispersive equations with variable coefficients via pseudodifferential calculus.. Our results are the natural generalization of smoothing effects of Schrodinger-type equations.