中文摘要：

利用极大算子线性化和对偶的方法,当曲线和象征分别满足适当的增长条件时,在维数n=2和n≥3的情形下,分别给出与一类广义色散方程 {itu＋φ（√-Δ）u=0,（x,t）∈R^n×R, u（x,0）=f（x） 的解相关的沿曲线极大算子的估计,其中φ（√-Δ）是具有象征为φ（｜ξ｜）的拟微分算子.

英文摘要：

Using the method of linearization of the maximal operator and duality,when curve and symbol respectively satisfied appropriate growth conditions,in the case of dimension n=2 and n≥3,we gave the estimation of maximal operator along curve associated with solution to a class of generalized dispersive equations {itu＋φ（√-Δ）u=0,（x,t）∈R^n×R, u（x,0）=f（x） where φ（√-Δ） was a pseudo-differential operator with symbol of φ（｜ξ｜）.