Available in electronic format
Available in print format		 Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Local and global $ C$-regularity

Author(s): Nihat Gökhan Gögüs
Journal: Trans. Amer. Math. Soc. 360 (2008), 2693-2707.
MSC (2000): Primary 32U15
Posted: December 11, 2007
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: A bounded domain $ D$ is called $ c$-regular if the plurisubharmonic envelope of every continuous function on $ \overline D$ extends continuously to $ \overline D$. We show using Gauthier's Fusion Lemma that a domain is locally $ c$-regular if and only if it is $ c$-regular.

References:

[C]
J. B. Conway, A course in functional analysis, Springer-Verlag, New York, 1990. MR 1070713 (91e:46001)

[CCW]
M. Carlehed, U. Cegrell and F. Wikström, Jensen measures, hyperconvexity and boundary behaviour of the pluricomplex Green function, Ann. Polon. Math. 71 (1999), no. 1, 87-103. MR 1684047 (2000a:32075)

[G]
P. M. Gauthier, Approximation by (pluri)subharmonic functions: Fusion and localization, Canad. J. Math. 44 (1992), no. 5, 941-950. MR 1186474 (93i:32018)

[Go]
N. G. Gogus, Continuity of Plurisubharmonic Envelopes, Ann. Polon. Math. 86 (2005), no.3, 197-217. MR 2207634

[I]
S. Ishikawa, Fixed points and iterations of a nonexpansive mapping in Banach space, Proc. Amer. Math. Soc. 59, (1976), 65-71. MR 0412909 (54:1030)

[K]
M. Klimek, Pluripotential Theory, Oxford Sci. Publ., 1991. MR 1150978 (93h:32021)

[KrP]
S. G. Krantz and H. R. Parks, A primer of real analytic functions, Second edition, Birkhäuser Advanced Texts, 1992. MR 1182792 (93j:26013)

[P1]
E. A. Poletsky, Plurisubharmonic functions as solutions of variational problems, Proc. Symp. Pure Math., 52, Part 1 (1991), 163-171. MR 1128523 (92h:32022)

[P2]
E. A. Poletsky, Holomorphic currents, Indiana Univ. Math. J., 42, no. 1 (1993), 85-144. MR 1218708 (94c:32007)

[P3]
E. A. Poletsky, Analytic geometry on compacta in $ {\mathbb{C}}^n$, Math. Z. 222 (1996), no. 3, 407-424. MR 1400200 (97e:32015)

[Po]
Ch. Pommerenke, Boundary behaviour of conformal maps, Springer-Verlag, Berlin, 1992. MR 1217706 (95b:30008)

[R]
T. Ransford, Potential theory in the complex plane, London Mathematical Society Student Texts, 28. Cambridge University Press, Cambridge, 1995. MR 1334766 (96e:31001)

[S]
N. Sibony, Une classe de domaines pseudoconvexes, Duke Math. J. 55 (1987), 299-319. MR 894582 (88g:32036)

[Wa]
J. Walsh, Continuity of envelopes of plurisubharmonic functions, J. Math. and Mech., Vol. 18, No.2 (1968), 143-148. MR 0227465 (37:3049)

[W]
F. Wikström, Jensen measures and boundary values of plurisubharmonic functions, Ark. Mat, 39 (2001), 181-200. MR 1821089 (2002b:32053)

Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 32U15

Retrieve articles in all Journals with MSC (2000): 32U15

Additional Information:

Nihat Gökhan Gögüs
Affiliation: Department of Mathematics, 215 Carnegie Hall, Syracuse University, Syracuse, New York 13244
Address at time of publication: Faculty of Engineering and Natural Sciences, Sabanci University, Orhanli, Tuzla, 34956, Istanbul, Turkey
Email: nggogus@syr.edu, nggogus@sabanciuniv.edu

DOI: 10.1090/S0002-9947-07-04400-5
PII: S 0002-9947(07)04400-5
Received by editor(s): October 28, 2005
Received by editor(s) in revised form: August 2, 2006
Posted: December 11, 2007
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google