Beltrami equations L¯t(g)=μ(·,t)Lt(g) on S3 (where Lt, |t|1, are the Rossi operators i.e., Lt spans the globally nonembeddable CR structure H(t) on S3 discovered by H. Rossi) are derived such that to describe quasiconformal mappings f:S3→N⊂C2 from the Rossi sphere S3,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 gt such that gt−v∈WF1,2S3,θ with v∈CR∞S3,H(0).
