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

Norisuke Ioku, Kazuhiro Ishige, Eiji Yanagida

研究成果: Article査読

9 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)2764-2783
ページ数20
ジャーナルJournal of Functional Analysis
264
12
DOI
出版ステータスPublished - 2013 6 15
外部発表はい

ASJC Scopus subject areas

  • Analysis

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