Sharp decay estimates of Lq-norms for nonnegative Schrödinger heat semigroups

Norisuke Ioku, Kazuhiro Ishige, Eiji Yanagida

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

Let H=-δ+V be a nonnegative Schrödinger operator on L2(RN), where N≥3 and V is a radially symmetric nonpositive function in RN decaying quadratically at the space infinity. For any 1≤p≤q≤∞, we denote by {norm of matrix}e-tH{norm of matrix}q,p the operator norm of the Schrödinger heat semigroup e-tH from Lp(RN) to Lq(RN). In this paper, under suitable conditions on V, we give the exact and optimal decay rates of {norm of matrix}e-tH{norm of matrix}q,p as t→∞ for all 1≤p≤q≤∞. The decay rates of {norm of matrix}e-tH{norm of matrix}q,p depend on whether the operator H is subcritical or critical and on the behavior of the positive harmonic function for the operator H.

Original languageEnglish
Pages (from-to)2764-2783
Number of pages20
JournalJournal of Functional Analysis
Volume264
Issue number12
DOIs
Publication statusPublished - 2013 Jun 15

Keywords

  • L-L estimates
  • Quadratically decaying potential
  • Schrödinger heat semigroups

ASJC Scopus subject areas

  • Analysis

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