On Gevrey vectors of some partial differential operators

References

• Cordaro PD, Himonas A. Global analytic regularity for sums of squares of vector fields. Trans Am Math Soc. 1998;350:4993–5001.
   Web of Science ®Google Scholar
• Himonas A, Petronilho G. On gevrey regularity of globally c∞-hypoelliptic operators. J Differ Equ. 2004;207:267–284.
   Web of Science ®Google Scholar
• Maire H. Hypoelliptic overdetermined systems of partial differential equations. Commun Partial Differ Equ. 1980;5:331–380.
   Google Scholar
• Baouendi MS. Sur une classe d’operateurs elliptiques dégénérés. Bulletin S M F. 1967;95:45–87.
   Google Scholar
• Hörmander L. The analysis of linear partial differential operators. Berlin: Springer Verlag; 1985.
   Google Scholar
• Treves F. Introduction to pseudodifferential and fourier integral operators. Vol. 1, New-York (NY): Plenum Press; 1981.
   Google Scholar
• Bove A, Tartakoff D. Optimal nonisotropic gevrey exponents for sums of squares of vector fields. Commun Partial Differ Equ. 1997;22:1263–1282.
   Web of Science ®Google Scholar
• Zanghirati L. Iterate di operatori e regolarita gevrey microlocale anisotropa. Rend Sem Mat Univ Padora. 1982;67:85–104.
   Google Scholar
• Hörmander L. Hypoelliptic second order differential equations. Acta Math. 1967;119:147–171.
   Web of Science ®Google Scholar
• Kohn JJ. Hypoellipticity and loss of derivatives, with an appendix by M. Derridj and D. Tartakoff. Ann Math. 2005;162:943–986.
   Google Scholar
• Morrey C, Nirenberg L. On the analyticity of the solutions of linear elliptic systems of partial differential equations. Commun Pure Appl Math. 1957;10:271–290.
   Web of Science ®Google Scholar
• Aronszajn N. Sur les decompositions des fonctions analitiques uniformes et sur leurs applications. Acta Math. 1935;65:1–156.
   Google Scholar
• Liess O, Rodino L. Fourier integral operators and inhomogeneous Gevrey classes. Ann Mat Pura Appl. 1988;150:167–262.
   Web of Science ®Google Scholar
• Bolley P, Camus J, Rodino L. Hypoellipticité analytique-Gevrey et itérés d’operateurs. Rend Sem Mat Univ Pol Torino. 1987;45:1–61.
   Google Scholar
• Nelson E. Analytic vectors. Ann Math. 1959;70:572–615.
   Web of Science ®Google Scholar
• Rothschild L, Stein E. Hypoelliptic differential operators and nilpotent groups. Acta Math. 1977;137:248–315.
   Web of Science ®Google Scholar
• Baouendi MS, Treves F. A property of the functions and distributions annihilated by a locally integrable system of complex vector fields. Ann Math. 1981;113:341–421.
   Web of Science ®Google Scholar
• Bolley P, Camus J, Mattera C. Analyticité microlocale et itérés d’operateurs. Sem Goulaouic Schwartz. 1978--1979;13:1–9.
   Google Scholar
• Baouendi MS, Metivier G. Analytic vectors of hypoelliptic operators of principal type. Am J Math. 1982;104:287–320.
   Web of Science ®Google Scholar
• Metivier G. Propriété des itérés et ellipticité. Commun Partial Differ Equ. 1978;3:827–876.
   Google Scholar
• Baouendi MS, Goulaouic C. Non-analytic hypoellipticity for some degenerate operators. Bull Am Math Soc. 1972;78:483–486.
   Web of Science ®Google Scholar
• Helffer B, Mattera C. Analyticité et itérés réduits d’un systĕ de champs de vecteurs. Commun Partial Differ Equ. 1980;5:1065–1072.
   Google Scholar
• Derridj M. Sur une classe d’opérateurs differentiels hypoelliptiques ā coefficients analytiques. Sem Goulaouic-Schwartz. 1970--1971;12. p. 6.
   Google Scholar
• Kohn JJ. Lectures on degenerate elliptic problems, CIME Bressanone 1977. In: Avantaggiati A, editor. Pseudo differential operators with applications. Berlin: Springer; 1978. p. 89–151.
   Google Scholar
• Baouendi MS, Goulaouic C. Régularité analytique et itérés d’opérateurs elliptiques dégénérés. Applications J Funct Anal. 1972;9:208–248.
   Google Scholar
• Castellanos JE, Cordaro PD, Petronilho G. Gevrey vectors in involutive tube structures and gevrey regularity for the solutions to certain classes of semilinear systems. J D’Anal Math. 2013;119:333–364.
   Web of Science ®Google Scholar
• Derridj M. On microlocal regularity for involutive systems of complex vector fields of tube type. Anal Geom MIMS-GGTM. 2014.
   Google Scholar
• Derridj M, Helffe B. Subellipticity and maximal hypoellipticity for two complex vector fields in (2+2) variables. Vol. 550, Contemporary mathematics, Geometric analysis of several complex variables, Marrakech Workshop. Providence (RI): American Mathematical Society; May 10--14. 2010.
   Google Scholar
• Journé JL, Trepreau JM. Hypoellipticité sans sous ellipticité: le cas des système de n champs de vecteurs complexes en (n+1 variables. Seminaire E.D.P. Ecole Polytechnique, April. 2006.
   Google Scholar
• Treves F. Study of a model in the theory of complexes of pseudodifferential operators. Ann Math. 1976;104:269–324. See also erratum In: \textit{Ann Math.} 1981;113:423.
   Web of Science ®Google Scholar
• Derridj M. Subelliptic estimates for some systems of complex vector fields, Trends in Mathematics. In: Padula M, Zanghirati L, editors. Hyperbolic Problems and Regularity Questions. Basel: Birkhauser; 2006;101–108.
   Google Scholar
• Barostichi RF, Cordaro PD, Petronilho G. Annalytic vectors in locally integrable structures. Contemp Math Am Math Soc. 2011;550:1–14.
   Google Scholar
• Derridj M, Zuily C. Sur la régularité gevrey des opérateurs de Hörmander. J Math Pures Appl. 1973;52:309–336.
   Web of Science ®Google Scholar
• Matsuzawa T. Sur les equations utt + tαuxx, α > 0. Nagoya Math J. 1971;42:43–55.
   Google Scholar
• Tartakoff D. The local real analyticity of solutions for □b and the ∂‾-Neumann problem. Acta Math. 1981;145:177–204.
   Web of Science ®Google Scholar
• Treves F. Analytic hypoellipticity of a class of pseudodifferential operators with double characteristics. Commun Partial Differ Equ. 1978;3:475–642.
   Google Scholar
• Derridj M, Tartakoff D. Local analyticity for □b and the ∂‾-Neumann problem at certain weakly pseudoconvex points. Commun Partial Differ Equ. 1988;13:1521–1600.
   Web of Science ®Google Scholar
• Bove A, Tartakoff D. Gevrey hypoellipticity for sums of squares with a non-homogeneous degeneracy. Proc Am Math Soc. 2014;142:1315–1320.
   Web of Science ®Google Scholar
• Rodino L, Zanghirati L. Pseudodifferential operators with multiple characteristics and Gevrey classes. Commun Partial Differ Equ. 1986;11:673–711.
   Web of Science ®Google Scholar
• Bove A, Treves F. On the gevrey hypoellipticity of sums of squares of vector fields. Ann Inst Fourier. 2004;54:1443–1475.
   Web of Science ®Google Scholar
• Lions JL, Magenes E. Problemès aux Limites Non-homogènes et Applications. Vols. 1--3, Paris: Dunod; 1968.
   Google Scholar
• Braun Rodriguez N, Chinni G, Cordaro PD, et al. Lower order perturbation and global analytic vectors for a class of globally analytic hypoelliptic operators. Proc Am Math Soc. Forthcoming 2016.
   Web of Science ®Google Scholar
• Derridj M. On the Gevrey vectors of L. Hörmander’s operators. 2016, preprint.
   Google Scholar