Abstract
We construct holomorphic support functions on a smoothly bounded, convex domain of finite type in ℂn which satisfy sharp, nonisotropic estimates near the fixed boundary point where the functions vanish.
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References
H. Boas and E. Straube, On equality of line type and variety type of real hypersurfaces in C“n, J. Geo. Anal. 2 (1992), 95–98.
J. Bruna, A. Nagel and S. Wainger, Convex hypersurfaces and Fourier transforms, Ann. of Math. 127 (1988), 333–365.
J.P. D’ Angelo Real hypersurfaces, orders of contact, and applications, Ann. of Math. 115 (1982), 615–637.
K. Diederich and J.E. Fornæss, Strictly pseudohyperbolic domains, manuscripta math. 25 (1978), 263–278.
K. Diederich and J.E. Fornæss, Support functions for convex domains of finite type, Math. Z. 230 (1999), 145–164.
K. Diederich, B. Fischer and J.E. Fornæss, Hölder estimates on convex domains of finite type, Math. Z. (to appear) 1998.
K. Diederich, J.E. Fornæss and J. Wiegerinck, Sharp Hölder estimates for∂ on ellipsoids, manuscripta math. 56 (1986) 399–417.
K. Diederich and G. Herbort, Pseudoconvex domains of semiregular type, Aspects of Math. 26 (1994), 127–162.
K. Diederich & G. Herbort, Estimated support functions on semiregular domains, Preprint 1997.
K. Diederich and E. Mazzilli, Zero varieties for the Nevanlinna class on all convex domains of finite type, Preprint 1998.
K. Diederich and E. Mazzilli, Extending holomorphic functions in convex domains 1998.
J.E. Fortress and N. Sibony, Construction of P.S.H. functions on weakly pseudo-convex domains, Duke Math. J. 58 (1989), 633–655.
E. Mazzilli, Un Exemple d’obstruction géométrique à l’extension des fonctions holomorphes bornées Lelong Proceedings (to appear).
J.D. McNeal, Convex domains of finite type, J. Func. Anal. 108 (1992), 361–373.
M. Range, The Caratheodory metric and holomorphic maps on a class of weakly pseudoconvex domains, Pac. J. Math. 78 (1978), 173–189.
J.Y. Yu, Multitype of convex domains Ind. Univ. Math. J. 41 (1992), 837–849.
J.Y. Yu, Peak functions on weakly pseudoconvex domains Ind. Univ. Math. J. 43 (1994), 1271–1295.
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Diederich, K., McNeal, J.D. (2000). Pointwise nonisotropic support functions on convex domains. In: Dolbeault, P., Iordan, A., Henkin, G., Skoda, H., Trépreau, JM. (eds) Complex Analysis and Geometry. Progress in Mathematics, vol 188. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8436-5_13
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DOI: https://doi.org/10.1007/978-3-0348-8436-5_13
Publisher Name: Birkhäuser, Basel
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