In this paper we consider several variants of the pointwise convergence problem for the Schrödinger equation, which generalize the previously known results.

Abstract. We consider Strichartz estimates for the wave equation with respect to general measures which satisfy certain growth conditions. In R 3+1 we obtain the sharp estimate and in higher dimensions improve the previous results.

Abstract. Recently, L. Guth improved the restriction estimate for the surfaces with strictly positive Gaussian curvature in R 3 . In this paper we extend his restriction estimate to the surfaces with strictly negative Gaussian curvature.