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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
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
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/S0002-9939-2011-10927-4
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