Strichartz type estimates in mixed Besov spaces with application to critical nonlinear Schrödinger equations

We study the Cauchy problem for the nonlinear Schrödinger 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 Schrödinger equations in mixed Besov spaces.