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L 2 estimates and existence theorems for the tangential Cauchy-Riemann complex

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References

  1. Andreotti, A., Hill, C.D.: Levi, E.E. Convexity and the Hans Lewy problem, I and II. Ann. Sc. Norm. Super. Pisa26, 325–363, 747–806 (1971)

    Google Scholar 

  2. Boutet de Monvel, L.: Integration des equations de Cauchy-Riemann induites formelles. Séminaire Goulaouic-Lions-Schwartz. Exposé IX (1974–1975)

  3. Boutet de Monvel, L., Sjöstrand, J.: Sur la singularité des noyaux de Bergman et de Szegö. Soc. Math. France Astérisque34–35, 123–164 (1976)

    Google Scholar 

  4. Burns, D.M.: Global behavior of some tangential Cauchy-Riemann equations. Proc. Conf. Park City, Utah, 1977. Lect. Notes Pure Appl. Math. 48, pp. 51–56. New York: Dekker 1979

    Google Scholar 

  5. Folland, G.B., Kohn, J.J.: The Neumann problem for the Cauchy-Riemann complex. Ann. Math. Stud. Princeton, NJ: Princeton Univ. Press 1972

    Google Scholar 

  6. Folland, G.B., Stein, E.M.: Estimates for the\(\bar \partial _b\)-complex and analysis on the Heisenberg group. Commun. Pure Appl. Math.27, 429–522 (1974)

    Google Scholar 

  7. Friedrichs, K.: The identity of weak and strong extensions of differential operators. Trans. Am. Math. Soc.55, 132–151 (1944)

    Google Scholar 

  8. Harvey, R., Polking, J.: Fundamental solutions in complex analysis I, II. Duke Math. J.47, 253–300, 301–340 (1979)

    Google Scholar 

  9. Henkin, G.M.: Solutions with bounds of the equations of H. Lewy and Poincaré-Lelong. In: Construction of functions of Nevanlinna class with given zeros in a strictly pseudo-convex domain. Dokl. Akad. Nauk SSSR224, 771–774 (1975) [English Transl.: Sov. Math., Dokl.16, 1310–1314 (1976)]

    Google Scholar 

  10. Henkin, G.M.: The Lewy equation and analysis of pseudo-convex manifolds. Usp. Mat. Nauk32, 57–118 (1977) [English Transl.: Russ. Math. Surv.32, 59–130 (1977)]

    Google Scholar 

  11. Hörmander, L.: Linear partial differential operators. New York: Springer 1963

    Google Scholar 

  12. Hörmander, L.:L 2 estimates and existence for the\(\bar \partial\) operators. Acta. Math.113, 89–152 (1965)

    Google Scholar 

  13. Hörmander, L.: An introduction to complex analysis in several variables. Princeton: Van Nostrand 1966

    Google Scholar 

  14. Kohn, J.J.: Boundaries of complex manifolds. Proc. Conf. on complex manifolds, Minneapolis. New York: Springer 1965

    Google Scholar 

  15. Kohn, J.J.: Global regularity for\(\bar \partial\) on weakly pseudo-convex manifolds. Trans. Am. Math. Soc.181, 272–292 (1973)

    Google Scholar 

  16. Kohn, J.J., Nirenberg, L.: Noncoercive boundary value problems. Commun. Pure. Appl. Math.18, 443–492 (1965)

    Google Scholar 

  17. Kohn, J.J., Rossi, H.: On the extension of holomorphic functions from the boundary of a complex manifold. Ann. Math.81, 451–472 (1965)

    Google Scholar 

  18. Kuranishi, M.: Strongly pseudo-convexCR structures over small balls, I, II. Ann. Math.115, 451–500 (1982) ibid Ann. Math.116, 1–64 (1982)

    Google Scholar 

  19. Rosay, J.P.: Equation de Lewy-résolubilite globale de l'équation ∂ b u =f sur la frontiére de domaines faiblement pseudo-convexes de ℂ2 (ou ℂn). Duke Math. J.49, 121–128 (1982)

    Google Scholar 

  20. Rossi, H.: Attaching analytic spaces to an analytic space along a pseudo-concave boundary. Proc. Conf. on Complex Analysis, Minneapolis, pp. 242–253 (1964)

  21. Shaw, M.-C.: A simplification of Rosay's theorem on global solvability of tangential Cauchy-Riemann equations. Illinois J. Math. (to appear)

  22. Shaw, M.-C.: Global solvability and regularity for\(\bar \partial\) on an annulus between two weakly pseudo-convex domains. Trans. Am. Math. Society (to appear)

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Shaw, MC. L 2 estimates and existence theorems for the tangential Cauchy-Riemann complex. Invent Math 82, 133–150 (1985). https://doi.org/10.1007/BF01394783

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