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Complex vector fields and hypoelliptic partial differential operators. (English) Zbl 1197.35083

Authors’ abstract: We prove a subelliptic estimate for systems of complex vector fields under some assumptions that generalize the essential pseudoconcavity for CR manifolds, that was first introduced by two of the authors, and the Hörmander’s bracket condition for real vector fields. Applications are given to prove the hypoellipticity of first order systems and second order partial differential operators. Finally we describe a class of compact homogeneous CR manifolds for which the distribution of \((0,1)\) vector fields satisfies a subelliptic estimate.

MSC:

35H20 Subelliptic equations
35H10 Hypoelliptic equations
32V20 Analysis on CR manifolds
35B45 A priori estimates in context of PDEs
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References:

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