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

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.