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

Hoepfner, G.; Hounie, J.; dos Santos, L.

doi:10.1090/S0002-9939-2011-10927-4

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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