This paper presents an abstract Strichartz estimate that leads to new endpoint Strichartz estimates for the wave and Schrödinger equations in higher dimensions. The authors prove that under certain energy and decay conditions, specific space-time norms are controlled by these estimates. The results are applied to show local existence for nonlinear wave equations and to derive Strichartz-type estimates for more general dispersive equations and the kinetic transport equation. The paper introduces the concept of σ-admissible exponent pairs and shows that for sharp σ-admissible pairs, the estimates hold under both untruncated and truncated decay conditions. The endpoint Strichartz estimates for the wave and Schrödinger equations in dimensions $ n \geq 4 $ and $ n \geq 3 $, respectively, are established as a consequence of these results. The authors also provide corollaries that demonstrate the well-posedness of the wave and Schrödinger equations under these estimates. For the wave equation, they show that solutions are continuous in time in Sobolev spaces, and for the Schrödinger equation, they show that solutions are in $ L^q $ and $ C $ spaces. These results are derived using the abstract Strichartz estimates and interpolation techniques. The paper further discusses applications of these estimates to other problems, including the kinetic transport equation and general dispersive equations. The results are shown to be robust under various transformations and can be extended to different types of equations. The authors conclude that the abstract Strichartz estimates provide a powerful framework for analyzing dispersive equations and their solutions.This paper presents an abstract Strichartz estimate that leads to new endpoint Strichartz estimates for the wave and Schrödinger equations in higher dimensions. The authors prove that under certain energy and decay conditions, specific space-time norms are controlled by these estimates. The results are applied to show local existence for nonlinear wave equations and to derive Strichartz-type estimates for more general dispersive equations and the kinetic transport equation. The paper introduces the concept of σ-admissible exponent pairs and shows that for sharp σ-admissible pairs, the estimates hold under both untruncated and truncated decay conditions. The endpoint Strichartz estimates for the wave and Schrödinger equations in dimensions $ n \geq 4 $ and $ n \geq 3 $, respectively, are established as a consequence of these results. The authors also provide corollaries that demonstrate the well-posedness of the wave and Schrödinger equations under these estimates. For the wave equation, they show that solutions are continuous in time in Sobolev spaces, and for the Schrödinger equation, they show that solutions are in $ L^q $ and $ C $ spaces. These results are derived using the abstract Strichartz estimates and interpolation techniques. The paper further discusses applications of these estimates to other problems, including the kinetic transport equation and general dispersive equations. The results are shown to be robust under various transformations and can be extended to different types of equations. The authors conclude that the abstract Strichartz estimates provide a powerful framework for analyzing dispersive equations and their solutions.