论文标题
关于与Schrodinger操作员相关的方函数和半组最大功能的换向器的加权紧凑性
On weighted Compactness of Commutators of square function and semi-group maximal function associated to Schrodinger operator
论文作者
论文摘要
在本文中，我们调查的目的是以下与Schrödinger运营商相关的Littlewood-Paley Square $ G $ $ L =-Δ+V $，该函数由以下方式定义： $ g（f）（x）= \ big（\ int_ {0}^{\ infty} \ big | | \ frac {d} {dt} {dt} e^{ - tl}（f）（x）\ big |^big |^2tdt \ big） $ V $是无负的潜力。我们表明，$ g $的换向器是紧凑型运营商，从$ l^p（w）$到$ l^p（w）$，$ 1 <p <\ infty $如果$ b \ in {\ rm cmo}_θ（ρ）$ in a_p^{ρ，θ} $，$ is $ cm cmm cm cm cm cm cm cm cm cm cm cm cm cm cm cm cm cm cm cm cms $ {\ rm bmo}_θ（ρ）$更大的$ {\ rm bmo}_θ（ρ）$更大的$ {\ rm cmo} $ {\ rm cmo} $ space和$ a_p^$ atep，$ a { 班级。对于由$ \ Mathcal {t}^*（f）（x）= \ sup_ {t> 0} | e^{ - tl} f（x）f（x）f（x）|。$。$。$。$。$。$。$。$。$。$。
In this paper, the object of our investigation is the following Littlewood-Paley square function $g$ associated with the Schrödinger operator $L=-Δ+V$ which is defined by: $g(f)(x)=\Big(\int_{0}^{\infty}\Big|\frac{d}{dt}e^{-tL}(f)(x)\Big|^2tdt\Big)^{1/2},$ where $Δ$ is the laplacian operator on $\mathbb{R}^n$ and $V$ is a nonnegative potential. We show that the commutators of $g$ are compact operators from $L^p(w)$ to $L^p(w)$ for $1<p<\infty$ if $b\in {\rm CMO}_θ(ρ)$ and $w\in A_p^{ρ,θ}$, where ${\rm CMO}_θ(ρ)$ is the closure of $\mathcal{C}_c^\infty(\mathbb{R}^n)$ in the ${\rm BMO}_θ(ρ)$ topology which is more larger than the classical ${\rm CMO}$ space and $A_p^{ρ,θ}$ is a weights class which is more larger than Muckenhoupt $A_p$ weight class. An extra weight condition in a privious weighted compactness result is removed for the commutators of the semi-group maximal function defined by $\mathcal{T}^*(f)(x)=\sup_{t>0}|e^{-tL}f(x)|.$
