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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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