Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

On the Mergelyan approximation property on pseudoconvex domains in $\mathbb{C}^{n}$

Author(s): Sanghyun Cho
Journal: Proc. Amer. Math. Soc. 126 (1998), 2285-2289.
MSC (1991): Primary 32F20, 32H40
MathSciNet review: 1459114
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: Let $\Omega$ be a smoothly bounded pseudoconvex domain of finite type in $\mathbb{C}^{n}$ . We prove the Mergelyan approximation property in various topologies on $\Omega$ when the estimates for $\overline{\partial }$ -equation are known in the corresponding topologies.

References:

1.: Catlin, D.W., Global regularity of the $\overline{\partial }$ -Neumann problem, Proc. Sympos. Pure Math. 41 (1984), 39-49. MR 85j:32033
2.: Chang, D.C., Nagel, A. and Stein, E., Estimates for the $\overline{\partial }$ -Neumann problem in pseudoconvex domains of finite type in $\mathbb{C}^{2}$ , Acta Math. 169 (1992), 153-228. MR 93k:32025
3.: Cho, S., Extension of complex structures on weakly pseudoconvex compact complex manifolds with boundary, Math. Z. 211 (1992), 105-119. MR 94h:32030
4.: H. R. Cho, S. Cho, and K. H. Shon, Stability of the estimates for $\overline{\partial }$ -equation on compact pseudoconvex complex manifolds, Kyushu J. Math. 48-1 (1994), 19-34. MR 95k:32017
5.: Cho, H.R. and Cho, S., Holomorphic approximation on compact pseudoconvex complex manifolds, J. of Geom. Anal. (to appear).
6.: Cho, S., Ahn, H. and Kim, S., Stability of Hölder estimates for $\overline{\partial }$ on pseudoconvex domains of finite type in $\mathbb{C}^{2}$ , Nagoya Math. J. (to appear).
7.: Fefferman, C. and Kohn, J.J., Hölder estimates on domains of complex dimension two and on three dimensional CR manifolds, Adv. Math. 69 (1988), 233-303. MR 89g:32027
8.: Fefferman, C., Kohn, J.J. and Machedon, M., Hölder estimates on CR manifolds with diagonalizable Levi form, Adv. Math. 84 (1990), 1-90. MR 92a:32019
9.: G. M. Henkin, Integral representations of functions which are holomorphic in strictly pseudoconvex regions, and some applications, Math. Sb. 78 (1969), 611-632; , Engl. Transl.: Math. USSR. Sb. 7 (1969), 597-616. MR 40:2902
10.: N. Kerzman, Hölder and $L^{p}$ estimates for solutions of $\overline{\partial }u=f$ in strongly pseudoconvex domains, Comm. Pure Appl. Math. 24 (1971), 301-379. MR 43:7658
11.: I. Lieb, Ein Approximationssatz auf streng pseudokonvexen Gebieten, Math. Ann. 184 (1969), 56-60. MR 41:7146
12.: Range, R.M., Integral kernels and Hölder estimates for $\overline{\partial }$ on pseudoconvex domains of finite type in $\mathbb{C}^{2}$ , Math.Ann. 288 (1990), 63-74. MR 91j:32018

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|