Maximal estimates for the bilinear Riesz means on Heisenberg groups

Abstract

In this article, we investigate the maximal bilinear Riesz means $S_{\ast }^{\hat{I}\pm }$ associated to the sublaplacian on the Heisenberg group. We prove that the operator $S_{\ast }^{\hat{I}\pm }$ is bounded from $L^{p_1}\times L^{p_2}$ into for $2\le p_1,p_2\le \infty$ and $1/p=1/p_1+1/p_2$ when is large than a suitable smoothness index $\hat{I}\pm (p_1,p_2)$. For obtaining a lower index $\hat{I}\pm (p_1,p_2)$, we define two important auxiliary operators and investigate their $L^p$ estimates,which play a key role in our proof.

arXiv admin note: text overlap with arXiv:1712.09238