Class of hypocomplex structures on the two-dimensional torus

Meziani, Abdelhamid; Zugliani, Giuliano

doi:10.1090/proc/14674

Class of hypocomplex structures on the two-dimensional torus
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Proc. Amer. Math. Soc. 147 (2019), 3937-3946 Request permission

Abstract:

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

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