an:07102556
Zbl 1421.35050
Meziani, Abdelhamid; Zugliani, Giuliano
Class of hypocomplex structures on the two-dimensional torus
EN
Proc. Am. Math. Soc. 147, No. 9, 3937-3946 (2019).
00438103
2019
j
35F05 35A01 35C15
complex vector fields; first integrals; theta function; global solvability; similarity principle; H??lder solvability; Cauchy-Pompeiu type integral operator
Summary: We study the H??lder 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.