DECAY ESTIMATES FOR SCHRODINGER HEAT SEMIGROUP WITH INVERSE SQUARE POTENTIAL IN LORENTZ SPACES II

Let H := -Delta + V be a nonnegative Schro center dot dinger operator on L-2(R-N), where N >= 2 and V is a radially symmetric inverse square potential. Let parallel to V(alpha)e(-tH)parallel to((Lp,sigma -> Lq,theta)) be the operator norm of del(alpha-tH)(e) from the Lorentz space L-p,L-sigma (R-N) to L-q,L-theta (R-N), where alpha is an element of{0, 1, 2, ... }. We establish both of upper and lower decay estimates of parallel to V(alpha)e(-tH)parallel to((Lp,sigma -> Lq,theta)) and study sharp decay estimates of parallel to V(alpha)e(-tH)parallel to((Lp,sigma -> Lq,theta)). Furthermore, we characterize the Laplace operator- increment from the view point of the decay of parallel to V(alpha)e(-tH)parallel to((Lp,sigma -> Lq,theta)).