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arXiv · 1712.09238

Bilinear Riesz means on the Heisenberg group

Heping Liu·Min Wang
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Abstract

In this article, we investigate the 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 $1\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 $α(p_{1},p_{2})$. There are some essential differences between the Euclidean space and the Heisenberg group for studying the bilinear Riesz means problem. We make use of some special techniques to obtain a lower index $α(p_{1},p_{2})$.

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Heping Liu, Min Wang. 2017-12-26. Bilinear Riesz means on the Heisenberg group. https://arxiv.org/abs/1712.09238

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