Bulletin of the American Mathematical Society

Integration of complex vector fields

J. J. Kohn

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc., Volume 78, Number 1 (1972), 1-11.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.bams/1183533388

Mathematical Reviews number (MathSciNet)
MR0298704

Zentralblatt MATH identifier
0228.35016

Subjects
Primary: 3548 3530

Citation

Kohn, J. J. Integration of complex vector fields. Bull. Amer. Math. Soc. 78 (1972), no. 1, 1--11. https://projecteuclid.org/euclid.bams/1183533388


Export citation

References

  • 1. A. Andreotti and C. D. Hill, Complex characteristic coordinates and tangential Cauchy-Riemann equations, Ann. Scuola Norm. Sup. Pisa (to appear).
  • 2. P. E. Conner, The Neumann's problem for differential forms on Riemannian manifolds, Mem. Amer. Math. Soc. No. 20 (1956). MR 17, 1197.
  • 3. K. O. Friedrichs, Differential forms on Riemannian manifolds, Comm. Pure Appl. Math. 8 (1955), 551-590. MR 19, 407.
  • 4. G. B. Folland, Tangential Cauchy-Riemann complex on a sphere in Cn, Doctoral Dissertation, Princeton University, Princeton, N.J., 1971.
  • 5. V. Guillemin and S. Sternberg, Subelliptic estimates for complexes, Proc. Nat. Acad. Sci. U.S.A. 67 (1970), 271-274.
  • 6. V. V. Grušin, On a class of hypoelliptic operators, Mat. Sb. 83 (125) (1970), 456-473 = Math. USSR Sb. 12 (1970), 458-476.
  • 7. L. Hörmander, An introduction to complex analysis in several variables, Van Nostrand, Princeton, N.J., 1966. MR 34 #2933.
  • 8. L. Hörmander, The Frobenius-Nirenberg theorem, Ark. Mat. 5 (1965), 425-432. MR 31 #2480.
  • 9. L. Hörmander, Differential equations without solutions, Math. Ann. 140 (1960), 169-173. MR 26 #5279.
  • 10. L. Hörmander, Hypoelliptic second order differential equations, Acta Math. 119 (1967), 147-171. MR 36 #5526.
  • 11. N. Kerzman, Hölder and $L\spp$ estimates for solutions of $\bar \partial u=f$ in strongly pseudoconvex domains., Comm. Pure Appl. Math. 24 (1971), 301-379.
  • 12. K. Kodaira, Harmonic fields in Riemannian manifolds (generalized potential theory), Ann. of Math. (2) 50 (1949), 587-665. MR 11, 108.
  • 13. J. J. Kohn, Harmonic integrals on strongly pseudo-convex manifold. I, II, Ann. of Math. (2) 78 (1963), 112-148; ibid. (2) 79 (1964), 450-472. MR 27 #2999; 34 #8010.
  • 14. J. J. Kohn, Boundaries of complex manifolds, Proc. Conf. Complex Analysis (Minneapolis, Minn., 1964), Springer, Berlin, 1965, pp. 81-94. MR 30 #5334.
  • 15. J. J. Kohn, Complex hypoelliptic equations, Proc. Conf. on Hypo-Elliptic Operators, Rome, 1971.
  • 16. J. J. Kohn and L. Nirenberg, Non-coercive boundary value problems, Comm. Pure Appl. Math. 18 (1965), 443-492. MR 31 #6041.
  • 17. J. J. Kohn, Pseudo-differential operators and non-elliptic problems, Pseudo-Differential Operators (C.I.M.E., Stresa, 1968), Edizioni Cremonese, Rome, 1969, pp. 157-165. MR 41 #3972.
  • 18. J. J. Kohn and H. Rossi, On the extension of holomorphic functions from the boundary of a complex manifold, Ann. of Math. (2) 81 (1965), 451-472. MR 31 #1399.
  • 19. M. Kuranishi, Convexity conditions related to 1/2-estimates in elliptic complexes, Proc. Internat. Congress of Math., Nice, 1970.
  • 20. H. Lewy, On the local character of the solutions of an atypical linear differential equation in three variables and a related theorem for regular functions of two complex variables, Ann. of Math. (2) 64 (1956), 514-522. MR 18, 473.
  • 21. H. Lewy, An example of a smooth linear partial differential equation without solution, Ann. of Math. (2) 66 (1957), 155-158. MR 19, 551.
  • 22. B. Malgrange, Pseudo-groupes de Lie elliptiques, Séminaire les équation aux derivées parielles I, College de France 1969-1970.
  • 23. A. Newlander and L. Nirenberg, Complex analytic coordinates in almost complex manifolds, Ann. of Math. (2) 65 (1957), 391-404. MR 19, 577.
  • 24. R. Nirenberg, On the H. Lewy extension phenomenon, Trans. Amer. Math. Soc. (to appear).
  • 25. R. Nirenberg, A complex Frobenius theorem, Seminar on Analytic Functions, Institute of Advanced Studies, 1957, pp. 172-189.
  • 26. L. Nirenberg and F. Treves, On local solvability of linear partial differential equations. I: Necessary conditions; II: Sufficient conditions, Comm. Pure Appl. Math. 23 (1970), 1-38, 459-510.
  • 27. E. V. Radkevič, Hypoelliptic operators with multiple characteristics, Mat. Sb. 79 (121) (1969), 193-216 = Math. USSR Sb. 8 (1969), 181-205. MR 41 #5763.
  • 28. B. L. Reinhart, Harmonic integrals on almost product manifolds, Trans. Amer. Math. Soc. 88 (1958), 243-276. MR 21 #3687.
  • 29. H. Rossi, Differentiable manifolds in complex euclidean space, Proc. Internat. Congress Math. (Moscow, 1966), "Mir", Moscow, 1968, pp. 512-516; Proc. Nat. Acad. Sci. U.S.A. 67 (1970), 271-274. MR 38 #2816.
  • 30. D. C. Spencer, Overdetermined systems of linear partial differential equations, Bull. Amer. Math. Soc. 75 (1969), 179-239. MR 39 #3533.
  • 31. W. J. Sweeney, A noncompact Dirichlet norm, Proc. Nat. Acad. Sci. U.S.A. 58 (1967), 2193-2195. MR 37 #3587.
  • 32. F. Treves, Hypoelliptic partial differential equations of principal type with analytic coefficients, Comm. Pure Appl. Math. 23 (1970), 637-651.