论文标题
高阶Riesz在逆高斯环境和UMD BANACH空间中转换
Higher order Riesz transforms in the inverse Gaussian setting and UMD Banach spaces
论文作者
论文摘要
在本文中，我们研究了高阶Riesz转换与$ \ \ m athbb {r}^n $上的$π^{n/2} e^{| x |^2} dx $给出的反向高斯度量相关的。我们建立$ l^p（\ mathbb {r}^n，e^{| x |^2} dx）$ - 有限属性属性，并获得表示高级riesz转换的主值单数积分作为主值。通过Riesz的转换和涉及反向高斯环境的操作员的虚构功能，具有UMD特性的Banach空间的新特征。
In this paper we study higher order Riesz transforms associated with the inverse Gaussian measure given by $π^{n/2}e^{|x|^2}dx$ on $\mathbb{R}^n$. We establish $L^p(\mathbb{R}^n,e^{|x|^2}dx)$-boundedness properties and obtain representations as principal values singular integrals for the higher order Riesz transforms. New characterizations of the Banach spaces having the UMD property by means of the Riesz transforms and imaginary powers of the operator involved in the inverse Gaussian setting are given.
