Class of hypocomplex structures on the two-dimensional torus

Class of hypocomplex structures on the two-dimensional torus

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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Veröffentlicht in:Proceedings of the American Mathematical Society 2019-09, Vol.147 (9), p.3937-3946
Hauptverfasser: Meziani, Abdelhamid, Zugliani, Giuliano
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/14674