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On the extension of $h^{p}$-CR distributions defined on rough tubes


Authors: G. Hoepfner, J. Hounie and L. A. Carvalho dos Santos
Journal: Proc. Amer. Math. Soc. 140 (2012), 627-633
MSC (2010): Primary 32A35, 32V25, 35N10; Secondary 42B30
DOI: https://doi.org/10.1090/S0002-9939-2011-10927-4
Published electronically: June 17, 2011
MathSciNet review: 2846332
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Abstract: We consider rough tubes $X+i\mathbb R^m\subset \mathbb {C}^m$ and generalized $CR$ functions in $L^\infty (X,h^p(\mathbb R^m))$, where $h^p(\mathbb R^m)$, $0<p<\infty$, is Goldberg’s semilocal Hardy space. We show that if $X$ is arcwise connected by rectifiable arcs, 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 the authors.


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Additional Information

G. Hoepfner
Affiliation: Departamento de Matemática, Universidade Federal de São Carlos, São Carlos, SP, 13565-905, Brasil
MR Author ID: 768261
ORCID: 0000-0002-4639-7539
Email: hoepfner@dm.ufscar.br

J. Hounie
Affiliation: Departamento de Matemática, Universidade Federal de São Carlos, São Carlos, SP, 13565-905, Brasil
MR Author ID: 88720
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

Keywords: Baouendi-Treves approximation formula, Hardy spaces, CR functions
Received by editor(s): September 1, 2010
Received by editor(s) in revised form: September 7, 2010, and December 1, 2010
Published electronically: June 17, 2011
Additional Notes: Work supported in part by CNPq and FAPESP
Communicated by: Franc Forstneric
Article copyright: © Copyright 2011 American Mathematical Society