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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Tube structures, Hardy spaces and extension of CR distributions


Authors: G. Hoepfner, J. Hounie and L. A. Carvalho dos Santos
Journal: Trans. Amer. Math. Soc. 363 (2011), 5091-5109
MSC (2000): Primary 32A35, 32V25, 35N10; Secondary 42B30
DOI: https://doi.org/10.1090/S0002-9947-2011-05138-X
Published electronically: May 11, 2011
MathSciNet review: 2813409
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Abstract: We consider rough tubes $ X+i\mathbb{R}^m\subset\mathbb{C}^m$, where $ X\subset \mathbb{R}^m$ is a measurable set, and extend the notion of $ CR$ function to the space $ L^\infty(X,h^p(\mathbb{R}^m))$, where $ h^p(\mathbb{R}^m)$, $ 0<p<\infty$, is Goldberg's semilocal Hardy space. We show that if $ X$ is the image of some connected manifold by some $ C^1$ map, then all such $ CR$ functions can be extended to the convex hull of the tube as $ CR$ functions $ \in L^\infty(\mathrm{ch}(X),h^p(\mathbb{R}^m))$. This extends previous work of Boggess.


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Additional Information

G. Hoepfner
Affiliation: Departamento de Matemática, Universidade Federal de São Carlos, São Carlos, SP, 13565-905, Brasil
Email: hoepfner@dm.ufscar.br

J. Hounie
Affiliation: Departamento de Matemática, Universidade Federal de São Carlos, São Carlos, SP, 13565-905, Brasil
Email: hounie@dm.ufscar.br

L. A. Carvalho dos Santos
Affiliation: Departamento de Matemática, Universidade Federal de São Carlos, São Carlos, SP, 13565-905, Brasil
Email: luis@dm.ufscar.br

DOI: https://doi.org/10.1090/S0002-9947-2011-05138-X
Keywords: Locally integrable structures, Baouendi-Treves approximation formula, Hardy spaces, CR functions
Received by editor(s): May 11, 2009
Published electronically: May 11, 2011
Additional Notes: This work was supported in part by CNPq and FAPESP
Article copyright: © Copyright 2011 American Mathematical Society