Analysis & PDE
- Anal. PDE
- Volume 6, Number 2 (2013), 371-445.
Hypoellipticity and nonhypoellipticity for sums of squares of complex vector fields
In this paper we consider a model sum of squares of complex vector fields in the plane, close to Kohn’s operator but with a point singularity,
The characteristic variety of is the symplectic real analytic manifold . We show that this operator is -hypoelliptic and Gevrey hypoelliptic in , the Gevrey space of index , provided , for every . We show that in the Gevrey spaces below this index, the operator is not hypoelliptic. Moreover, if , the operator is not even hypoelliptic in . This fact leads to a general negative statement on the hypoellipticity properties of sums of squares of complex vector fields, even when the complex Hörmander condition is satisfied.
Anal. PDE, Volume 6, Number 2 (2013), 371-445.
Received: 28 August 2011
Revised: 16 January 2012
Accepted: 13 February 2012
First available in Project Euclid: 20 December 2017
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Bove, Antonio; Mughetti, Marco; Tartakoff, David. Hypoellipticity and nonhypoellipticity for sums of squares of complex vector fields. Anal. PDE 6 (2013), no. 2, 371--445. doi:10.2140/apde.2013.6.371. https://projecteuclid.org/euclid.apde/1513731313