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Agmon, S., Douglis, A. &Nirenberg,L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, IComm. Pure Appl. Math., 12 (1959), 623–727; II,ibid., 17 (1964), 35–92.
Ash, M. E., The basic estimate of the\(\bar \partial \)-Neumannn problem in the non-Kählerian case.Amer. J. Math., 86 (1964), 247–254.
Baouendi, M. S. &Goulaouic, C., Analyticity for degenerate elliptic equations and applications.Proc. Symposia in Pure Math., 23 (1971), 79–84.
Boutet De Monvel, L., Comportement d'un opérateur pseudo-differentiel sur une variété à bord, I, II.,J. Anal. Math., 17 (1966), 241–304.
Conner, P. E., The Neumann's problem for differential forms on Riemannian manifolds.Mem. Amer. Math. Soc., 20, 1956.
Derridj, M., Sur la régularité Gevrey jusqu'au bord des solutions du problème de Neumann pour\(\bar \partial \).Proc. Symposia in Pure Math., 30:1 (1977), 123–126.
Derridj, M. &Tartakoff, D. S., On the global real analyticity of solutions to the\(\bar \partial \)-Neumann problem.Comm. Partial Differential Equations, 1 (1976), 401–435.
Derridj, M. & Tartakoff, D. S. Sur la régularité locale des solutions du problème de Neumann pour\(\bar \partial \).Journées sur les fonctions analytiques, in Springer Lecture Notes in Math., 578, 1977, 207–216.
Dynin, A., Pseudodifferential operators on Heisenberg groups. To appear.
Folland, G. B. & Kohn, J. J.,The Neumann Problem for the Cauchy-Riemann Complex. Annals of Math. Studies Number 75, Princeton, 1972.
Folland, G. B. &Stein, E. M., Estimates for the\(\bar \partial _b \) complex and analysis on the Heisenberg group.Comm. Pure Appl. Math., 27 (1974), 429–522.
Garabedian, P. &Spencer, D. C., Complex boundary value problems.Trans. Amer. Math. Soc., 73 (1952), 223–242.
Greiner, P. C. & Stein, E. M., Estimates for the\(\bar \partial \)-Neumann Problem Princeton, 1977.
Hörmander, L., Fourier integral operators, I.,Acta Math., 128 (1971), 79–183.
—,Linear partial Differential Operators. Springer Verlag, New York, 1963.
—, Pseudo-differential operators and non-elliptic boundary problems.Ann. of Math., 83 (1966), 129–209.
—,An Introduction to Complex Analysis in Several Variables, Van Nostrand, Princeton, 1966.
Kohn, J. J., Harmonic integrals on strongly pseudoconvex manifolds, I.Ann. of Math., 78 (1963), 112–148; II,Ibid., 79 (1964), 450–472.
—, Boundaries of complex manifolds.Proc. Conf. on Complex Manifolds (Minneapolis), Springer-Verlag, New York, 1965.
Kohn, J. J. &Nirenberg L., Non-coercive boundary value problems.Comm. Pure Appl. Math., 18 (1965), 443–492.
Kohn, J. J. &Spencer, D. C., Complex Neumann problems.Ann. of Math., 66 (1957), 89–140.
Komatsu, G., Global analytic-hypoellipticity of the\(\bar \partial \)-Neuman problemTôhoku Math. J. Ser. 2, 28 (1976), 145–156.
Morrey, C. B. &Nirenberg, L., On the analyticity of the solutions of linear elliptic systems of partial differential equations.Comm. Pure Appl. Math., 10 (1957), 271–290.
Nirenberg, L.,Lectures on Partial Differential Equations. Texas Technical Univ., Lubbock, 1972.
Sato, M., Kawai, T. & Kashiwara, M.,Microfunction and Pseudo-differential Equations. Lecture notes in Mathematics 287, Springe 1973, 265–529.
Tartakoff, D. S., Gevrey hypoellipticity for subelliptic boundary value problems.Comm. Pure Appl. Math., 26 (1973), 251–312.
—, On the global real analyticity of solutions to □ b .Comm. Partial Differential Equations 1 (1976), 283–311.
—, Local Gevrey and quasianalytic hypoellipticity for □ b .Bull. Amer. Math. Soc., 82 (1976), 740–742.
Tartakoff, D. S., Remarks on the intersection of certain quasianalytic classes and the quasianalytic hypoellipticity of □ b To appear.
—, Local analytic hypoellipticity for □ b on non-degenerate Cauchy-Riemann manifolds.Proc. Nat. Acad. Sci. U.S.A., 75:7 (1978), 3027–3028.
Trèves, F., Analytic hypo-ellipticity of a class of peudodifferential operators with double characteristics and applications to the\(\bar \partial \)-Neumann problem.Comm. Partial Differential Equations, 3:6–7 (1978), 475–642.
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Tartakoff, D.S. The local real analyticity of solutions to □ b and the \(\bar \partial \)-Neumann problem. Acta Math. 145, 177–204 (1980). https://doi.org/10.1007/BF02414189
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DOI: https://doi.org/10.1007/BF02414189