LITTLEWOOD-PALEY THEOREM FOR SCHR(O)DINGER OPERATORS

Let H be a Schr(o)dinger operator on Rn. Under a polynomial decay condition for the kernel of its spectral operator, we show that the Besov spaces and Triebel-Lizorkin spaces associated with H are well defined. We further give a Littlewood-Paley characterization of Lp spaces in terms of dyadic functions of H. This generalizes and strengthens the previous result when the heat kernel of H satisfies certain upper Gaussian bound.     

TIME DECAY FOR SCHR(O)DINGER EQUATION WITH ROUGH POTENTIALS

We obtain certain time decay and regularity estimates for 3D Schrodinger equation with a potential in the Kato class by using Besov spaces associated with Schrodinger operators.