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We consider rough tubes X+iRm ⊂ Cm and generalized CR functions in L∞(X,hp(Rm)), where hp(Rm), 0 < p < ∞, 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 ∈ L∞(ch(X), hp(Rm)). This extends previous work of the authors.

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