Class of hypocomplex structures on the two-dimensional torus
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- by Abdelhamid Meziani and Giuliano Zugliani PDF
- 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.References
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Additional Information
- Abdelhamid Meziani
- Affiliation: Department of Mathematics and Statistics, Florida International University, Miami, Florida 33199
- MR Author ID: 239413
- Email: meziani@fiu.edu
- Giuliano Zugliani
- Affiliation: Departamento de Matemática, Universidade Federal de São Carlos, São Carlos–SP, 13565-905 Brazil
- MR Author ID: 1237158
- Email: giuzu@dm.ufscar.br
- Received by editor(s): January 10, 2019
- Published electronically: June 10, 2019
- Additional Notes: The second author was supported by FAPESP (grant 2017/00848-0).
- Communicated by: Joachim Krieger
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 3937-3946
- MSC (2010): Primary 35A01, 35C15, 35F05, 58J99
- DOI: https://doi.org/10.1090/proc/14674
- MathSciNet review: 3993786