On Pointwise Convergence for Schrodinger Operator in a Convex Domain

摘要

In this paper, we prove that the maximal inequality sup | t|< 1 | ei t D f ( x, y)| L2 loc( ) = C f HsD ( ),. f. HsD ( ) holds for any s > 1 2 with = {( x, y). R2 | x > 0} and D =. 2 x + ( 1 + x). 2 y. As a direct application, we obtain the pointwise convergence for the free Schrodinger equation i. tu + Du = 0 with initial data u( 0) = f inside strictly convex domain.