We study the Cauchy problem for the nonlinear Schrodinger equation with power nonlinearity in the fractional order Sobolev space H^s(Rn). We consider the case where the nonlinear term is H^s-critical and the differentiability thereof is less than s. We prove the existence of time global solutions of the Cauchy problem for small initial data. To this end, we prove Strichartz type estimates for linear inhomogeneous Schrodinger equations in mixed Besov spaces.