Abstract
The solvability of the equation \(Lu=f\) is considered for a hypocomplex vector field L in \({\mathbb {R}}^2\). When L satisfies a Łojasiewiczproperty,the solutions can be represented through a generalization of the Cauchy integral operator. The results in \({\mathbb {R}}^2\) are then used to study a class of degenerate complex structures in \({\mathbb {R}}^{2n}\) generated by a system of hypocomplex vector fields \(L_1,\cdots ,L_n\). The use of the Cauchy integral operator is used to study the solvability of the underlying differential complex \({\mathbb {L}}\).
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Meziani, A. Cauchy Integral Operator in Complex Structures with Degeneracies. J Geom Anal 33, 26 (2023). https://doi.org/10.1007/s12220-022-01073-0
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DOI: https://doi.org/10.1007/s12220-022-01073-0