On the extension of $h^{p}$-CR distributions defined on rough tubes
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- by G. Hoepfner, J. Hounie and L. A. Carvalho dos Santos PDF
- Proc. Amer. Math. Soc. 140 (2012), 627-633 Request permission
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.References
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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
- 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
- © Copyright 2011 American Mathematical Society
- 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
- MathSciNet review: 2846332