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The Holomorphic Extension of H<LATEX><TEX>$^{p}$</TEX></LATEX>-CR Functions on Tube Submanifolds

Proceedings of the American Mathematical Society / v.127 no.5. 1999, pp.1427-1435

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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.

Keyword : Primary 32A35, 42B30, 32D99 . H$^{p}$ function . Tube submanifold

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