Vector valued Hardy spaces related to analytic functions having distributional boundary values

The Hardy space H^p of vector valued analytic functions in tubedomains in C^n and with values in Banach space are defined. Ana-lytic functions in tube domains inCnwith values in Hilbert space which have L^p functions with values in Hilbert space as distributional boundary value are proved to be in H^p. A Poisson integral representation for such vector valued analytic functions is obtained