This paper discusses the initial-boundary-value problems (IBVPs) of nonlinear Schrödinger equations posed in a half plane R × R + with nonhomogeneous Dirichlet boundary conditions. For any given s ≥ 0, if the initial data ϕ(x, y) are in Sobolev space H s (R × R + ) with the boundary data h(x, t) in an optimal space H s (0, T ) as defined in the introduction, which is slightly weaker than the spacethe local well-posedness of the IBVP in C([0, T ]; H s (R × R + )) is proved. The global well-posedness is also discussed for s = 1. The main idea of the proof is to derive a boundary integral operator for the corresponding nonhomogeneous boundary condition and obtain the Strichartz estimates for this operator. The results presented in the paper hold also for the IBVP posed in a half space R n × R + with any n > 1.2010 Mathematics Subject Classification. Primary 35Q55.It turns out, however, that the space W s (0, T ) is not the optimal choice. Indeed, as the trace of the solution v of the linear Schrödinger equation in R 2 ,most likely does not belong to the space W s (0, T ) (see the discussion in Section 2), we will show that the solution v possesses the following trace property (see Lemma 2.1 in Section 2):then the trace of the solution v ∈ C(R; H s (R 2 )), v b (x, t) = v(x, 0, t), belongs to the space H s (R 2 ) := ß w ∈ L 2 (R 2 ) : Ä 1 + |λ| + |ξ| 2 | ä s/2 λ + |ξ| 2 1/4 F[w](λ, ξ) ∈ L 2 (R 2 ) ™