关于Heisenberg群上的高阶Riesz变换
On the higher Riesz transforms for the Heisenberg group

利用Heisenberg群上的高阶Riesz变换定义, 结合L2空间函数的谱分解与特殊Hermite函数的性质, 获得该变换对应的卷积核. 进一步, 证明该卷积核满足Calder′on- Zygmund正则条件, 进而可推导Heisenberg高阶Riesz变换在Lp, 1 < p < ∞中有界, 并且是弱(1,1)型的.
： Using the definition of the higher Riesz transforms for Heisenberg group, together with the spectral decomposition of functions belong to L2 spaces and the properties of the special Hermite functions, we obtain the convolution kernels for these transforms. Moreover, we show that those kernels satisfy the Calder′on-Zygmund singular conditions, then one can deduce that the Heisenberg higher Riesz transforms are bounded on Lp, 1 < p < ∞, and are weak type (1,1)