与分数阶热半群相关的平方函数刻画Hardy空间  

The Characterizations of the Hardy Space via Square Functions Associated with Fractional Heat Semigroups

作　　者：王志永 赵凯 WANG Zhiyong;ZHAO Kai(School of Mathematics and Statistics,Qingdao University,Qingdao 266071,China)

机构地区：[1]青岛大学数学与统计学院,山东青岛266071

出　　处：《应用数学》2022年第2期394-401,共8页Mathematica Applicata

基　　金：山东省自然科学基金(ZR2020MA004)。

摘　　要：令L=-Δ+V是一个Schrödinger算子,V是一个满足逆Hölder不等式的非负位势.在本文中,首先引入由分数阶热半群{e^(-tL^(α))}t>0生成的Lusin面积函数,其次通过从属性公式和半群的正则性,我们用平方函数刻画与L相关的Hardy空间H^(n/(n+γ))_(L)(R^(n)).Assume that L=-Δ+V is a Schrödinger operator,where the nonnegative potential V satisfies a reverse Hölder inequality.In this paper,we first introduce the Lusin area functions generated by the fractional heat semigroup{e^(-t/L^(α))}t>0.Then by the reproducing formulas and the regularity properties of semigroups,we establish square function characterizations of the Hardy space H^(n(n+γ))_(L)(R^(n))associated with L.

关 键 词：分数阶热半群 HARDY空间 平方函数 Schrödinger算子 

分 类 号：O174[理学—数学]