Sums of squares III: Hypoellipticity in the infinitely degenerate regime

• Lyudmila Korobenko ^[1] ; Eric Sawyer ^[2]
  1. [1] Reed College

     Reed College

     Estados Unidos

     
  2. [2] McMaster University

     McMaster University

     Canadá

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 40, Nº 4, 2024, págs. 1249-1292
• Idioma: inglés
• DOI: 10.4171/RMI/1482
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• Resumen

  • This is the third paper in a series of three dealing with sums of squares and hypoellipticity in the infinitely degenerate regime. We establish a C2,δ generalization of M. Christ’s smooth sum of squares theorem, and then use a bootstrap argument with the sum of squares decomposition for matrix functions, obtained in our second paper of this series, to prove a hypoellipticity theorem that generalizes some cases of the results of Christ, Hoshiro, Koike, Kusuoka and Stroock and Morimoto for sums of squares, and of Fedĭi and Kohn for degeneracies not necessarily a sum of squares