References
Airapetyan, R.A., Henkin, G.M.: Integral representations of differential forms on Cauchy-Riemann manifolds and the theory of CR-functions Uspekhi Mat. Nauk 39, 39–106 (1984)
Boggess, A.: CR Manifolds, the Tangential Cauchy-Riemann Complex. CRC Press, 1991
Baouendi, M. S., Ebenfelt, P., Rothschild, L.P.: Real Submanifolds in Complex Space and their Mappings. Math. Series 47 Princeton University Press, Princeton, New Jersey, 1999
Beals, R., Greiner, P.C.: Calculus on Heisenberg Manifolds. Ann. Math. Studies 119, Princeton University Press, Princeton, New Jersey, 1988
Boutet de Monvel, L.: Hypoellipitic operators with double characteristics and related pseudodifferential operators. Commun. Pure Appl. Math. 27, 585–639 (1974)
Boutet de Monvel, L., Sjöstrand, J.: Sur la singularité des noyaux de Bergman et de Szegö. Société Mathématique de France, Astérisque, 34, 35, 123–164 (1976)
Caffarelli, L.A.: Interior a priori estimates for solutions of fully nonlinear equations. Ann. Math. 130, 189–213 (1989)
Caffarelli, L.A., Cabré, X.: Fully nonlinear elliptic equations. Am. Math. Society, Colloquium Publications, Providence, Rhode Island 43, 1995
Campanato, S.: Equazioni elittiche del secondo ordine e spazi Ann. Mat. Pura e Appl. 69, 321–380 (1965)
Chen, S.-C., Shaw, M.-C.: Partial Differential Equations in Several Complex Variables. American Math. Society-International Press, Studies in Advanced Mathematics, vol. 19, Providence, Rhode Island, 2001
Christ, M.: Lectures on Singular Integral Operators. American Math. Society, CBMS 77 Providence, Rhode Island, 1990
Coifman, R.R., Weiss, G.: Analyse harmonique non-commutative certains espaces homogenes. Lecture Notes in Math. 242, Springer-Verlag Berlin Heidelberg, New York, Tokyo
De Giorgi, E.: Frontiere orientate di misura minima. (Italian) Seminario di Matematica della Scuola Normale Superiore di Pisa, 1960-61
Evans, L.C.: Partial Differential Equations. Graudate Studies in Mathematics, vol. 19, Am. Math. Society Providence, RI, 1998
Fefferman, C.: The Bergman kernel and biholomorphic mappings of pseudoconvex domains. Invent. Math. 26, 1–65 (1974)
Fefferman, C., Kohn, J.J.: Hölder estimates on domains of complex dimension two and on three dimensional CR manifolds. Adv. Math. 69, 233–303 (1988)
Fefferman, C., Kohn, J.J., Machedon, M.: Hölder estimates on CR manifolds with a diagonalizable Levi form. Adv. Math. 84, 1–90 (1990)
Folland, G.B.: A fundamental solution for a subelliptic operator Bull. Am. Math. Soc. 79, 373–376 (1973)
Folland, G.B.: Subelliptic estimates and function spaces on nilpotent Lie groups. Ark. Mat. 13, 161–207 (1975)
Folland, G.B., Kohn, J.J.: The Neumann Problem for the Cauchy-Riemann Complex. Ann. Math. Studies 75, Princeton University Press, Princeton, NJ, 1972
Folland, G.B., Stein, E.M.: Estimates for the complex and analysis on the Heisenberg group. Commun. Pure Appl. Math. 27, 429–522 (1974)
Folland, G.B., Stein, E.M.: Hardy spaces of homogeneous groups. Princeton University Press, Princeton, NJ, 1982
Friedrichs, K.: The identity of weak and strong extensions of differential operators. Trans. Am. Math. Soc. 55, 132–141 (1944)
Giaquinta, M.: Multiple integrals in the calculus of variations and nonlinear elliptic systems. Annals Math. Studies, vol 105, Princeton University Press Princeton, NJ, 1983
Giaquinta, M.: Introduction to Regularity Theory for Nonlinear Elliptic Systems.Birkhäuser Basel, Boston, Berlin, 1993
Hill, C., Nacinovich, M.: Pseudoconcave CR manifolds. Complex Analysis and Geometry (Trento, 1993), Lecture Notes in Pure and Applied Math. Dekker, New York 173, 275–297 (1996)
Hörmander, L.: Weak and strong extensions of differential operators. Commun. Pure. Appl. Math. 14, 371–379 (1961)
Hörmander, L.: L2 estimates and existence theorems for the operator. Acta Math. 113, 89–152 (1965)
Hörmander, L.: Lp estimates for (pluri-)subharmonic functions. Math. Scand. 20, 147–171 (1967)
Hörmander, L.: Hypoelliptic second-order differential equations. Acta Math. 119, 65–78 (1967)
Hörmander, L.: The Analysis of Linear Partial Differential Operators III. Springer-Verlag, Berlin Heidelberg New York Tokyo, 1985
Jerison, D.: The Poincaré inequality for vector fields satisfying Hörmander’s condition. Duke Math. J. 53, 503–523 (1986)
Kohn, J.J.: Boundaries of complex manifolds 1965 Proc. Conf. Complex Manifolds (Minneapolis,1964), Springer-Verlag, New York, pp. 81–94
Kohn, J.J.: Microlocalization of CR structures. Several Complex Variables, (Proc. of the 1981 Hangzhou conf.) 1984 Birkhäuser, Boston, pp. 29–36
Kohn, J.J.: Estimates for on pseudoconvex CR manifolds. Proc. Symposia Pure Math. American Math. Soc. Providence, Rhode Island 43, 207–217 (1985)
Kohn, J.J., Nirenberg, L.: Noncoercive boundary value problems Commun. Pure Appl. Math. 18, 443–492 (1965)
Kohn, J.J., Rossi, H.: On the extension of holomorphic functions from the boundary of a complex manifold. Ann. Math. 81, 451–472 (1965)
Kerzman, N., Stein, E.M.: The Cauchy kernel, the Szegö kernel, and the Riemann mapping function. Math. Ann. 236, 85–93 (1978)
Krantz, S.G.: Geometric Lipschitz spaces and applications to complex function theory and nilpotent groups J. Funct. Anal. 34, 456–471 (1979)
Lions, J.-L., Magenes, E.: Non-Homogeneous Boundary Value Problems and Applications, Volume I. Springer-Verlag, New York, 1972
Macías, R., Segovia, C.: Lipschitz functions on spaces of homogeneous type. Adv. Math. 33, 257–270 (1979)
Nagel, A., Stein, E.M.: Lectures on pseudo-differential operators. Princeton University Press Princeton, New Jersey, 1979
Nagel, A., Stein, E.M., Wainger, S.: Balls and metrics defined by vector fields I: Basic properties. Acta Math. 155, pp. 103–147
Rothschild, L., Stein, E.M.: Hypoelliptic differential operators and nilpotent groups. Acta Math. 137, 247–320 (1976)
Shaw, M.-C.: Hypoellipticity of a system of complex vector fields. Duke Math. 50, 713–728 (1983)
Shlag, W.: Schauder and Lp estimates for parabolic systems via Campanato spaces. Commun. Part. Diff. Eq. 21, 1141–1175 (1996)
Stein, E.M.: Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals. Math. Series 43, Princeton University Press, Princeton, New Jersey, 1993
Taylor, M.E.: Pseudodifferential Operators. Math. Series 34, Princeton University Press Princeton, New Jersey, 1981
Treves, F.: Introduction to Pseudodifferential and Fourier Integral Operators, Volume I, Pseudodifferential Operators; Volume II, Fourier Integral Operators. Plenum Press, New York London, 1980
Treves, F.: Hypo-Analytic Structures: Local Theory. Math. Series 40, Princeton University Press, Princeton, New Jersey, 1992
Wang, L.: On the regularity theory of fully nonlinear parabolic equations II. Commun. Pure Appl. Math. 45, 141–178 (1992)
Wang, L.: A geometric approach to the Calderón-Zygmund estimates. Preprint
Author information
Authors and Affiliations
Corresponding author
Additional information
Partially supported by NSF grant DMS 01-00492.
Partially supported by NSF grant DMS 01-00679.
Rights and permissions
About this article
Cite this article
Shaw, MC., Wang, L. Hölder and Lp estimates for □ b on CR manifolds of arbitrary codimension. Math. Ann. 331, 297–343 (2005). https://doi.org/10.1007/s00208-004-0583-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00208-004-0583-5