Counterexamples to Strichartz Type Inequalities

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] The study of Strichartz s inequality is very important in the theory of nonlinear Shrodinger equations. The inequalities do not hold for all choice of constants. Many cases were settled. for instance, some cases were settled by Montegomery-Smith. In this paper we give a generalization to the usual Strichartz inequality using the Riesz potential. We then prove the inequality to hold in some cases and give counterexamples on other cases.