As we know, thus far, there has appeared no definition of bilinear spectral multipliers on Heisenberg groups. In this article, we present one reasonable definition of bilinear spectral multipliers on Heisenberg groups and investigate its boundedness. We find some restrained conditions to separately ensure its boundedness from \({{\cal C}_0}\left({{\mathbb{H}^n}} \right) \times {L^2}\left({{\mathbb{H}^n}} \right)\;{\rm{to}}\;{L^2}\left({{\mathbb{H}^n}} \right)\), from \({L^2}\left({{\mathbb{H}^n}} \right) \times {{\cal C}_0}\left({{\mathbb{H}^n}} \right)\;{\rm{to}}\;{L^2}\left({{\mathbb{H}^n}} \right)\), and from L^p × L^q to L^r with 2 < p, q < ∞, 2 ≤ r ≤ ∞.

众所周知，到目前为止，在海森堡群上还没有定义双线性谱乘数。在本文中，我们对Heisenberg群上的双线性谱乘数给出一个合理的定义，并研究其有界性。我们发现一些约束条件可以从\（{{\ cal C} _0} \ left（{{\ mathbb {H} ^ n}} \ right）\ times {L ^ 2} \ left（{{ \ mathbb {H} ^ n}} \ right）\; {\ rm {to}} \; {L ^ 2} \ left（{{\ mathbb {H} ^ n}} \ right）\），来自\ （{L ^ 2} \ left（{{\ mathbb {H} ^ n}} \ right）\ times {{\ cal C} _0} \ left（{{\ mathbb {H} ^ n}} \ right） \; {\ rm {to}} \; {L ^ 2} \ left（{{\ mathbb {H} ^ n}} \ right）\），然后从L ^p × L ^q到L ^r，其中2 < p ，q <∞，2≤ [R ≤∞。