The holomorphic extension of 𝐻^{𝑝}-CR functions on tube submanifolds

Boggess, Al

doi:10.1090/S0002-9939-99-04828-5

The holomorphic extension of $H^p$-CR functions on tube submanifolds
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Proc. Amer. Math. Soc. 127 (1999), 1427-1435 Request permission

Abstract:

We consider the set of CR functions on a connected tube submanifold of $C^n$ satisfying a uniform bound on the $L^p$-norm in the tube direction. We show that all such CR functions holomorphically extend to $H^p$ functions on the convex hull of the tube ($1 \leq p \leq \infty$). The $H^p$-norm of the extension is shown to be the same as the uniform $L^p$-norm in the tube direction of the CR function.

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