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Journal of the American Mathematical Society
ISSN 1088-6834(e) ISSN 0894-0347(p)

     

Quasianalyticity and pluripolarity

Author(s): Dan Coman; Norman Levenberg; Evgeny A. Poletsky
Journal: J. Amer. Math. Soc. 18 (2005), 239-252.
MSC (2000): Primary 26E10, 32U20; Secondary 32U35, 32U15, 32U05
Posted: January 18, 2005
MathSciNet review: 2137977
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Abstract | References | Similar articles | Additional information

Abstract: We show that the graph

\begin{displaymath}\Gamma_f=\{(z,f(z))\in{\mathbb{C}}^2:\,z\in S\}\end{displaymath}

in ${\mathbb{C}}^2$ of a function $f$ on the unit circle $S$ which is either continuous and quasianalytic in the sense of Bernstein or $C^\infty$ and quasianalytic in the sense of Denjoy is pluripolar.

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E. Bedford and B. A. Taylor, A new capacity for plurisubharmonic functions, Acta Math. 149 (1982), 1-40. MR 0674165 (84d:32024)

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J. P. Demailly, Mesures de Monge-Ampère et mesures plurisousharmoniques, Math. Z. 194 (1987), 519-564. MR 0881709 (88g:32034)

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K. Diederich and J. E. Fornæss, A smooth curve in $\mathbb{C}^2$ which is not a pluripolar set, Duke Math. J. 49 (1982), 931-936. MR 0683008 (85b:32025)

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Y. Katznelson, An Introduction to Harmonic Analysis, Dover Publications, New York, 1976. MR 0422992 (54:10976)

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M. Klimek, Pluripotential Theory, Oxford, Clarendon Press, 1991.MR 1150978 (93h:32021)

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N. Levenberg, G. Martin, E.A. Poletsky, Analytic disks and pluripolar sets, Indiana Univ. Math. J. 41 (1992), 515-532.MR 1183357 (93h:46075)

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S. Mandelbrojt, Sur les fonctions indéfinitement dérivables, Acta Math. 72 (1940), 15-35. MR 0001783 (1:297d)

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Additional Information:

Dan Coman
Affiliation: Department of Mathematics, 215 Carnegie Hall, Syracuse University, Syracuse, New York 13244
Email: dcoman@syr.edu

Norman Levenberg
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: nlevenbe@indiana.edu

Evgeny A. Poletsky
Affiliation: Department of Mathematics, 215 Carnegie Hall, Syracuse University, Syracuse, New York 13244
Email: eapolets@syr.edu

DOI: 10.1090/S0894-0347-05-00478-9
PII: S 0894-0347(05)00478-9
Keywords: Quasianalytic functions, pluripolar sets, pluripotential theory
Received by editor(s): December 2, 2002
Posted: January 18, 2005
Additional Notes: The first and the last authors were supported by NSF grants
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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