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Sobolev estimates for the Lewy operator on weakly pseudo-convex boundaries

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References

  1. Ahern, P., Schneider, R.: Holomorphic Lipschitz functions in pseudoconvex domains. Am. J. Math.101, 543–565 (1979)

    Google Scholar 

  2. Aizenberg, L.A., Dautov, Sh.A.: Differential forms orthogonal to holomorphic functions or forms, and their properties. Providence: Am. Math. Soc. 1983

    Google Scholar 

  3. Andreotti, A., Hill, C.D.: E.E. Levi convexity and the Hans Lewy problem, Parts I and II. Ann. Scuola Norm Sup. Pisa26, 325–363; 747–806 (1972)

    Google Scholar 

  4. Boas, H.P.: The Szegö projection: Sobolev estimates in regular domains. Preprint

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

    Google Scholar 

  6. Burns, Jr., D.M.: Global behavior of some tangential Cauchy-Riemann equations. In: Partial differential equations and geometry. Proc. Park City Conf., pp. 51–56. New York: Dekker 1979

    Google Scholar 

  7. Folland, G.B., Kohn, J.J.: The Neumann problem for the Cauchy-Riemann complex. Princeton: Princeton Univ. Press 1972

    Google Scholar 

  8. 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 

  9. Harvey, R., Polking, J.: Fundamental solutions in complex analysis, I and II. Duke Math. J.46, 253–300; 301–340 (1979)

    Google Scholar 

  10. Henkin, G.M.: The Lewy equation and analysis on pseudoconvex manifolds, I and II. Russ. Math. Surv.32, 59–130 (1977); Math. USSR-Sb.31, 63–94 (1977)

    Google Scholar 

  11. Hörmander, L.: Linear partial differential operators. Berlin, Heidelberg, New York: Springer 1976

    Google Scholar 

  12. Kerzman, N., Stein, E.M.: The Szegö kernel in terms of Cauchy-Fantappiè kernels. Duke Math. J.45, 197–224 (1978)

    Google Scholar 

  13. Kohn, J.J.: Boundaries of complex manifolds. Proc. Conf. Complex Analysis (Minneapolis), pp. 81–94. New York: Springer 1965

    Google Scholar 

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

    Google Scholar 

  15. Kohn, J.J.: Estimates for\(\bar \partial _b\) on pseudo-convex CR manifolds. In: Pseudodifferential operators and applications. Providence: Am. Math. Soc. 1985

    Google Scholar 

  16. 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 

  17. Lewy, H.: An example of a smooth linear partial differential equation without solution. Ann. Math.66, 155–158 (1957)

    Google Scholar 

  18. Phong, D.H., Stein, E.M.: Estimates for the Bergman and Szegö projections on strongly pseudoconvex domains. Duke Math. J.44, 695–704 (1977)

    Google Scholar 

  19. Rosay, J.P.: Equation de Lewy-résolubilité global de l'équation b u=f sur la frontière de domaines faiblement pseudo-convexes deC 2 (ouC n). 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. Complex Analysis (Minneapolis), pp. 242–253. New York: Springer 1965

    Google Scholar 

  21. Shaw, M.-C.:L 2 estimates and existence theorems for the tangential Cauchy-Riemann complex. Invent. math.82, 133–150 (1985)

    Google Scholar 

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

  23. Stein, E.M., Weiss, G.: Introduction to Fourier analysis on Euclidean spaces. Princeton: Princeton Univ. Press 1971

    Google Scholar 

  24. Kohn, J.J.: The range of the tangential Cauchy-Riemann operator. Preprint

  25. Henkin, G., Leiterer, J.: Theory of functions on complex manifolds. Basel: Birkhäuser 1984

    Google Scholar 

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Both authors partially supported by the National Science Foundation

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Boas, H.P., Shaw, MC. Sobolev estimates for the Lewy operator on weakly pseudo-convex boundaries. Math. Ann. 274, 221–231 (1986). https://doi.org/10.1007/BF01457071

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