Strong boundedness of analytic functions in tubes

Certain classes of analytic functions in tube domains TC= ￠ n+iC in n-dimensional complex space, where C is an open connected cone in ￠ n, are studied. We show that the functions have a boundedness property in the strong topology of the space of tempered distributions g ￠ € 2. We further give a direct proof that each analytic function attains the Fourier transform of its spectral function as distributional boundary value in the strong (and weak) topology of g ￠ € 2.