Decay rate of Lq norms of critical Schrödinger heat semigroups

Abstract

Let H:=−Δ+V be a critical Schrödinger operator on L2(R N), where N≥3 and V is a radially symmetric function decaying quadratically at the space infinity. We study the optimal decay rate of the operator norm of the Schrödinger heat semigroup e−tH from L2(RN) to Lq(RN) (2≤q≤∞).