Beltrami equations on Rossi spheres

Beltrami equation $overline{L}_t (g) = mu( cdot , t) L_t (g)$ on $S^3$ (where $L_t$, $t in (-1,1)$, are the Rossi operators i.e., $L_t$ spans the globally nonembeddable CR structure $mathcal{H} (t)$ on $S^3$ discovered by H. Rossi) are derived such that to describe quasiconformal mappings $f: S^3 to N subset mathbb{C}^2$ from the Rossi sphere $(S^3 , mathcal{H} (t))$. Using the Greiner-Kohn-Stein solution to the Lewy equation and the Bargmann representations of the Heisenberg group, we solve the Beltrami equations for Sobolev-type solutions $g_t$ such that $g_t - v in W^{1,2}_F (S^3, theta)$ with $v in CR^infty (S^3 , mathcal{H} (0))$.