Convergence of Solutions of General Dispersive Equations Along Curve

In this paper, the authors give the local L2 estimate of the maximal operator Sφ,γ* of the operator family {St,φ,γ} defined initially by ■which is the solution（when n = 1） of the following dispersive equations（*） along a curve γ:■where φ : R+→R satisfies some suitable conditions and φ(（-?）1/2) is a pseudo-differential operator with symbol φ（|ξ|）. As a consequence of the above result, the authors give the pointwise convergence of the solution（when n = 1） of the equation（*） along curve γ.Moreover, a global L2 estimate of the maximal operator Sφ,γ* is also given in this paper.