Lp norms of non-critical Schrödinger semigroups

https://doi.org/10.1016/0022-1236(91)90137-TGet rights and content
Under an Elsevier user license
open archive

Abstract

We consider Schrödinger semigroups etH, H = −Δ + V on Rn with V ~ −c¦x¦−2, as ¦x¦ → ∞, 0 < c < [(12)(n − 2)]2, with H ⩾ 0. We determine the exact power law divergence of ∥etHp, p and of some ∥etHq, p as maps from Lp to Lq. The results are expressed most naturally in terms of the power α for which there exists a positive resonance η such that Hη = 0, η(x) ~ ¦x¦−α.

Cited by (0)

Research partially funded under NSF Grant DMS-8801981.