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Loss of derivatives for systems of complex vector fields and sums of squares


Authors: Tran Vu Khanh, Stefano Pinton and Giuseppe Zampieri
Journal: Proc. Amer. Math. Soc. 140 (2012), 519-530
MSC (2010): Primary 32W05, 32W25, 32T25
DOI: https://doi.org/10.1090/S0002-9939-2011-11287-5
Published electronically: September 27, 2011
MathSciNet review: 2846320
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Abstract | References | Similar Articles | Additional Information

Abstract: We discuss, both for systems of complex vector fields and for sums of squares, the phenomenon discovered by Kohn of hypoellipticity with loss of derivatives.


References [Enhancements On Off] (What's this?)

  • 1. A. Bove, M. Derridj, J. J. Kohn and D. S. Tartakoff, Sums of squares of complex vector fields and (analytic-) hypoellipticity, Math. Res. Lett. 13, no. 5 (2006), 683-701. MR 2280767 (2007k:35051)
  • 2. D. Bell and S. Mohammed, An extension of Hörmander's theorem for infinitely degenerate second-order operators, Duke Math. J. 78 (1995), 453-475. MR 1334203 (96g:35034)
  • 3. M. Christ, Hypoellipticity of the Kohn Laplacian for three-dimensional tubular Cauchy-Riemann structures, J. of the Inst. of Math. Jussieu 1 (2002), 279-291. MR 1954822 (2003k:32048)
  • 4. V. S. Fedi, A certain criterion for hypoellipticity, Mat. Sb. 14 (1971), 15-45. MR 0287160 (44:4367)
  • 5. G. B. Folland and J. J. Kohn, The Neumann problem for the Cauchy-Riemann complex, Ann. Math. Studies 75, Princeton Univ. Press, Princeton, NJ (1972). MR 0461588 (57:1573)
  • 6. L. Hörmander, Hypoelliptic second order differential equations, Acta Math. 119 (1967), 147-171. MR 0222474 (36:5526)
  • 7. J. J. Kohn, Hypoellipticity at points of infinite type, Contemporary Math. 251, Amer. Math. Soc., Providence, RI, 2000, pp. 393-398. MR 1771281 (2001f:32066)
  • 8. J. J. Kohn, Superlogarithmic estimates on pseudoconvex domains and CR manifolds, Annals of Math. (2) 156 (2002), 213-248. MR 1935846 (2003i:32059)
  • 9. J. J. Kohn, Hypoellipticity and loss of derivatives, Annals of Math. (2) 162 (2005), 943-986. MR 2183286 (2006k:35036)
  • 10. J. J. Kohn and L. Nirenberg, Non-coercive boundary value problems, Comm. Pure Appl. Math. 18 (1965), 443-492. MR 0181815 (31:6041)
  • 11. S. Kusuoka and D. Stroock, Applications of Mallavain calculus II, J. Fac. Sci. Univ. Tokyo Sec. IA Math. 32 (1985), 1-76. MR 783181 (86k:60100b)
  • 12. Y. Morimoto, Hypoellipticity for infinitely degenerate elliptic operators, Osaka J. Math. 24 (1987), 13-35. MR 881744 (88m:35030)
  • 13. C. Parenti and A. Parmeggiani, On the hypoellipticity with a big loss of derivatives, Kyushu J. Math. 59 (2005), 155-230. MR 2134059 (2005m:35049)
  • 14. E. M. Stein, An example on the Heisenberg group related to the Lewy operator, Invent. Math. 69 (1982), 209-216. MR 674401 (84c:35031)
  • 15. D. S. Tartakoff, Analyticity for singular sums of squares of degenerate vector fields, Proc. Amer. Math. Soc. 134, no. 11 (2006), 3343-3352. MR 2231919 (2007h:35030)

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Additional Information

Tran Vu Khanh
Affiliation: Dipartimento di Matematica, Università di Padova, via Trieste 63, 35121 Padova, Italy
Email: khanh@math.unipd.it

Stefano Pinton
Affiliation: Dipartimento di Matematica, Università di Padova, via Trieste 63, 35121 Padova, Italy
Email: pinton@math.unipd.it

Giuseppe Zampieri
Affiliation: Dipartimento di Matematica, Università di Padova, via Trieste 63, 35121 Padova, Italy
Email: zampieri@math.unipd.it

DOI: https://doi.org/10.1090/S0002-9939-2011-11287-5
Received by editor(s): September 30, 2010
Published electronically: September 27, 2011
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2011 American Mathematical Society

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