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

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 t hat all such CR functions holomorphically extend to H-p functions on the co nvex hull of the tube (1 less than or equal to p less than or equal to 1). The H-p-norm of the extension is shown to be the same as the uniform L-p-no rm in the tube direction of the CR function.