LAUSR

. In the present paper, we give some characterization of the L 2 maximal estimate for the operator P ta,γ f (cid:0) Γ( x,t ) (cid:1) along curve with complex time, which is defined by where t,γ > 0 and a ≥ 2 , curve Γ is a function such that Γ : R × [0 , 1] → R , and satisfies H¨older’s condition of order σ and bilipschitz conditions. The authors extend the results of the Schr¨odinger type with complex time of Bailey [1] and Cho, Lee and Vargas [3] to Schr¨odinger operators along the curves.