论文标题
双线性riesz的最大估计值在海森堡组上表示
Maximal estimates for the bilinear Riesz means on Heisenberg groups
论文作者
论文摘要
在本文中，我们研究了最大的双线性riesz表示与海森伯格集团上的Sublaplacian相关的$ s^{α} _ {*} $。我们证明，操作员$ s^{α} _ {*} $从$ l^{p_ {p_ {1}} \ times l^{p_ {2}} $ to $％l^{p} $ to $％l^{p} $ for $ 2 \ leq p_ {1} $ 1/p = 1/p_ {1}+1/p_ {2} $当$％α$大于合适的平滑度索引$α（p_ {1}，p_ {2}）$时。为了获得较低的索引$α（p_ {1}，p_ {2}）$，我们定义了两个重要的辅助操作员，并调查其$ l^{p} $估计值，这在我们的证明中起着关键作用。
In this article, we investigate the maximal bilinear Riesz means $S^{α}_{*}$ associated to the sublaplacian on the Heisenberg group. We prove that the operator $S^{α}_{*}$ is bounded from $L^{p_{1}}\times L^{p_{2}}$ into $% L^{p}$ for $2\leq p_{1}, p_{2}\leq \infty $ and $1/p=1/p_{1}+1/p_{2}$ when $% α$ is large than a suitable smoothness index $α(p_{1},p_{2})$. For obtaining a lower index $α(p_{1},p_{2})$, we define two important auxiliary operators and investigate their $L^{p}$ estimates,which play a key role in our proof.
