A New Proof of Okaji’s Theorem for a Class of Sum of Squares Operators
Annales de l'Institut Fourier, Volume 59 (2009) no. 2, pp. 595-619.

Let P be a linear partial differential operator with analytic coefficients. We assume that P is of the form “sum of squares”, satisfying Hörmander’s bracket condition. Let q be a characteristic point for P. We assume that q lies on a symplectic Poisson stratum of codimension two. General results of Okaji show that P is analytic hypoelliptic at q. Hence Okaji has established the validity of Treves’ conjecture in the codimension two case. Our goal here is to give a simple, self-contained proof of this fact.

Soit P un opérateur différentiel analytique, de la forme “somme de carrés”, avec la condition d’Hörmander réalisée. Soit q un point caractéristique de P. On suppose que q est un point d’un “symplectic Poisson stratum” de codimension deux (au sens de Treves). D’après le théorème d’Okaji, P est hypoelliptique analytique en q. Autrement dit, la conjecture de Treves est vraie en codimension deux. On donne dans ce travail une preuve élémentaire de ce fait.

Received:
Revised:
Accepted:
DOI: 10.5802/aif.2442
Classification: 35H10,  35H20,  35A17,  35A20,  35A27
Keywords: Analytic hypoelliptic, sum of squares
Cordaro, Paulo D. 1; Hanges, Nicholas 2

1 Universidade de São Paulo São Paulo, SP (Brazil)
2 Lehman College Department of Mathematics/CUNY Bronx, New York 10468 (USA)
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Cordaro, Paulo D.; Hanges, Nicholas. A New Proof of Okaji’s Theorem  for a Class of Sum of Squares Operators. Annales de l'Institut Fourier, Volume 59 (2009) no. 2, pp. 595-619. doi : 10.5802/aif.2442. https://aif.centre-mersenne.org/articles/10.5802/aif.2442/

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