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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Subaveraging estimate for $CR$ functions
defined on a hypersurface $M$ of ${\mathrm{C}}^{n}$


Author: Victoria Paolantoni
Journal: Proc. Amer. Math. Soc. 126 (1998), 1733-1738
MSC (1991): Primary 32F99, 32D15; Secondary 58G17
MathSciNet review: 1459143
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Abstract: Let $M$ be a smooth real hypersurface of $\mathrm{C}^{n}$ and $N$ a compact submanifold of $M$. We generalize a result of A. Boggess and R. Dwilewicz giving, under some geometric conditions on $M$ and $N$, an estimate of the submeanvalue on $N$ of any $CR$ function $f$ on a neighbourhood of $N$, by the $L^{1}$ norm of $f$ on a neighbourhood of $N$ in $M$.


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Additional Information

Victoria Paolantoni
Affiliation: Centre de Mathématiques et Informatique, Université de Provence, 39, avenue Joliot Curie, 13453 Marseille Cédex 13, France
Email: paolanto@gyptis.univ-mrs.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04466-9
PII: S 0002-9939(98)04466-9
Keywords: Analytic disc, nonisotropic ball, finite type
Received by editor(s): November 26, 1996
Communicated by: Eric Bedford
Article copyright: © Copyright 1998 American Mathematical Society