Unconditional well-posedness for subcritical NLS in HS

Let n >= 3 and consider the subcritical nonlinear Schrodinger equation, i partial derivative(t)u + Delta u = |u|(alpha)u, with initial data u(0) is an element of H(s)(R(n)). When s >= 1, Kato proved that if a maximal solution exists, then it is unique in C([0, T(max)), H(s)). Previously, uniqueness had only been proven in strictly smaller subspaces. The existence of a solution is assured when s is an element of [0, 1], so that the subcritical nonlinear Schrodinger equation is unconditionally locally well-posed in H(1). We extend the uniqueness result so that the subcritical nonlinear Schrodinger equation is unconditionally locally well-posed in H(s) when s is an element of [n/2(n-1), 1].