ISOMORPHISMS OF VARIABLE HARDY SPACES ASSOCIATED WITH SCHR(O)DINGER OPERATORS

• 来源期刊: 数学物理学报（英文版）
• 年，卷（期）: 2021,（1）
• 页码范围: 39-66
• 页数: 28页
• 语种: 英文
• DOI: 10.3969/j.issn.0252-9602.2021.01.003

摘要

Let L:=-△+V be the Schr?dinger operator on Rn with n ≥ 3,where V is a non-negative potential satisfying △-1(V)∈ L∞(Rn).Let w be an L-harmonic function,determined by V,satisfying that there exists a positive constant δ such that,for any x ∈ Rn,0 ＜ δ ≤ w(x)≤ 1.Assume that p(.):Rn →(0,1]is a variable exponent satisfying the globally log-H?lder continuous condition.In this article,the authors show that the mappings HPL(.)(Rn)? f → wf ∈ Hp(.)(Rn)and Hp(.)(Rn)? f →(-△)1/2L-1/2(f)∈ Hp(.)(Rn)are isomorphisms between the variable Hardy spacesHPL(.)(Rn),associated with L,and the variable Hardy spacesHP(.)(Rn).