  In this paper, we explore the relations between different kinds of Strichartz
estimates and give new estimates in Euclidean space $\mathbb{R}^n$. In
particular, we prove the generalized and weighted Strichartz estimates for a
large class of dispersive operators including the Schr\"odinger and wave
equation. As a sample application of these new estimates, we are able to prove
the Strauss conjecture with low regularity for dimension 2 and 3.
