论文标题
Littlewood-Paley与一般Ornstein-Uhlenbeck Semigroups相关的功能
Littlewood-Paley functions associated with general Ornstein-Uhlenbeck semigroups
论文作者
论文摘要
在本文中，我们建立了$ l^p（\ mathbb {r}^d，γ_\ infty）$ - 涉及Ornstein-uhlenbeck semigroups的时间和空间衍生物的平方函数的有界属性。这里$γ_\ infty $表示不变的度量。为了证明$ 1 <p <\ infty $的强型结果，我们使用$ r $ boundedness。弱类型（1,1）的属性是通过研究为Square Littlewood-Paley函数定义的全球和本地运营商来确定的。顺便说一句，我们证明了$ l^p（\ mathbb {r}^d，γ_\ infty）$ - ornstein-uhlenbeck semogroups的最大和变异算子的界限属性。
In this paper we establish $L^p(\mathbb{R}^d,γ_\infty)$-boundedness properties for square functions involving time and spatial derivatives of Ornstein-Uhlenbeck semigroups. Here $γ_\infty$ denotes the invariant measure. In order to prove the strong type results for $1<p<\infty$ we use $R$-boundedness. The weak type (1,1) property is established by studying separately global and local operators defined for the square Littlewood-Paley functions. By the way we prove $L^p(\mathbb{R}^d,γ_\infty)$-boundedness properties for maximal and variation operators for Ornstein-Uhlenbeck semigroups.
