Heisenberg型群上的仿积算子

Paraproducts on Heisenberg Type Groups

首先给出了Heisenberg型群上一类仿积算子的定义,研究了该算子的L^2→L^2有界性.其次探讨了Heisenberg型群上的Calderon-Zygmund算子,包括该算子的L^p→L^p有界性,L^1→L^(1,∞)有界性以及H^1→L^1有界性.最后证明了仿积算子也是Calderon-Zygmund算子,同时还证明了仿积算子的一些其它重要性质.

We define a class of paraproducts on Heisenberg type groups. We prove they have L2 boundedness. We also study CalderSn-Zygmund operators, and prove they are bounded operators which map L^p to L^p, L^1 to L^1,∞ and H^1 to L^1. Then we prove the paraproducts are also CalderSn-Zygmund operators and they also satisfy two important properties that Pb= b and P^1 = 0 in the sense of distribution.