Strichartz type Inequalities for Parabolic and Schr\"odinger Equations in rearrangement invariant Spaces

In this paper we generalize the classical Strichartz estimation for solutions of initial problem for linear parabolic and Schr"odinger PDE on many popular classes {\it pairs} of rearrangement invariant(r.i.) spaces and construct some examples in order to show the exactness of our estimations.