The Heisenberg group and the group Fourier transform of regular homogeneous distributions

We calculate the group Fourier transform of regular homogeneous distributions defined on the Heisenberg group, ${\displaystyle H^n}$. All such distributions can be written as an infinite sum of terms of the form ${\displaystyle f(\theta ){\overline{w}}^{-k}P\left(z\right)}$, where ${\displaystyle (z,t)\in {ℂ}^n\times ℝ}$, ${\displaystyle w={\left|z\right|}^2-it}$, ${\displaystyle \theta =arg(\overline{\frac{w}{w}}}$ and P(z) is an element of an orthonormal basis for the spherical harmonics. The formulas derived give the Fourier transform of the distribution in terms of a smooth kernel of the variable θ and the Weyl correspondent of P.