Bilinear Bochner-Riesz Means on Métivier groups

In this paper, we study the $L^{p_1}(G) \times L^{p_2}(G)$ to $L^{p}(G)$ boundedness of the bilinear Bochner-Riesz means associated with the sub-Laplacian on Métivier group $G$ under the Hölder’s relation $1/p = 1/p_1 + 1/p_2$, $1\leq p_1, p_2 \leq \infty$. Our objective is to obtain boundedness results, analogous to the Euclidean setting, where the Euclidean dimension in the smoothness threshold is possibly replaced by the topological dimension of the underlying Métivier group $G$.

💡 Research Summary

The paper investigates the boundedness of bilinear Bochner‑Riesz means associated with the sub‑Laplacian on Métivier groups, a class of two‑step nilpotent Lie groups that strictly contains Heisenberg‑type groups. After recalling the classical Bochner‑Riesz problem in Euclidean space and its bilinear extension, the authors turn to the non‑commutative setting. A Métivier group G has Lie algebra g=g₁⊕g₂ with