Class of hypocomplex structures on the two-dimensional torus

This is the authors' abstract. We don't add key points for this paper.

We study the Hölder solvability of a class of complex vector fields on the torus T 2 T^2 . We make use of the Theta function to associate a Cauchy-Pompeiu type integral operator. A similarity principle for the solutions of the equation L u = a u + b u ¯ Lu=au+bū is obtained.