高阶薛定谔算子的无穷小相对有界性特征

IF 1.2 3区 数学 Q1 MATHEMATICS
Jun Cao , Mengyao Gao , Yongyang Jin , Chao Wang
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In this paper, the authors characterize the infinitesimal relative boundedness and Trudinger's subordination for <em>H</em> on <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span> with <span><math><mi>p</mi><mo>∈</mo><mo>[</mo><mn>1</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math></span>, via the limit behavior of the family of operators <span><math><msub><mrow><mo>{</mo><mi>V</mi><msup><mrow><mo>(</mo><msup><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mo>−</mo><mi>m</mi><mo>/</mo><mn>2</mn></mrow></msup><mo>}</mo></mrow><mrow><mi>λ</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></mrow></msub></math></span> and a generalized Kato-type class condition. The latter is weaker than the classical Kato class condition corresponding to the case <span><math><mi>p</mi><mo>=</mo><mn>1</mn></math></span>. 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引用次数: 0

摘要

设 m∈N 和 H=(-Δ)m/2+V 是欧几里得空间 Rn 中的高阶薛定谔算子,V∈Lloc1(Rn)。在本文中,作者通过算子{V(λ2-Δ)-m/2}λ∈(0,∞)族的极限行为和广义卡托类条件,描述了 H 在 p∈[1,∞]的 Lp(Rn)上的无穷小相对有界性和特鲁丁格从属性。后者弱于 p=1 情况下的经典加藤类条件。即使当 H=-Δ+V 是二阶薛定谔算子时,所有这些特征也是新的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Characterizations of infinitesimal relative boundedness for higher order Schrödinger operators
Let mN and H=(Δ)m/2+V be a higher order Schrödinger operators in the Euclidean space Rn with VLloc1(Rn). In this paper, the authors characterize the infinitesimal relative boundedness and Trudinger's subordination for H on Lp(Rn) with p[1,), via the limit behavior of the family of operators {V(λ2Δ)m/2}λ(0,) and a generalized Kato-type class condition. The latter is weaker than the classical Kato class condition corresponding to the case p=1. All these characterizations are new even when H=Δ+V is a second order Schrödinger operator.
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来源期刊
CiteScore
2.50
自引率
7.70%
发文量
790
审稿时长
6 months
期刊介绍: The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.
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