Weighted Strichartz Estimates with Angular Regularity and their   Applications
  In this paper, we establish an optimal dual version of trace estimate involving angular regularity. Based on this estimate, we get the generalized Morawetz estimates and weighted Strichartz estimates for the solutions to a large class of evolution equations, including the wave and Schr\"{o}dinger equation. As applications, we prove the Strauss' conjecture with a kind of mild rough data for $2\le n\le 4$, and a result of global well-posedness with small data for some nonlinear Schr\"{o}dinger equation with $L^2$-subcritical nonlinearity. 
Daoyuan Fang, Chengbo Wang