论文标题
通过Martingale Transforms的乘数定理
Multiplier theorems via martingale transforms
论文作者
论文摘要
我们开发了一种新方法来证明各种几何设置中的乘数定理。主要思想是使用Martingale变换和Gundy-Varopoulos表示形式来通过合适的扩展程序定义的乘数。在此过程中，我们提供了具有独立利益的Stinga和Torrea对结果的概括的概率证明。我们在这里的方法还恢复了二阶Riesz的尖锐$ l^p $界限，而riesz通过限制参数进行了变换。
We develop a new approach to prove multiplier theorems in various geometric settings. The main idea is to use martingale transforms and a Gundy-Varopoulos representation for multipliers defined via a suitable extension procedure. Along the way, we provide a probabilistic proof of a generalization of a result by Stinga and Torrea, which is of independent interest. Our methods here also recover the sharp $L^p$ bounds for second order Riesz transforms by a liming argument.
