A class of analytic functions in tube domains T C = ℝ n + i C in n -dimensional complex space, where C is an open connected cone in ℝ n , which has been defined by V. S. Vladimirov is studied. We show that a previously obtained L 2 growth estimate concerning these functions can be replaced by a pointwise growth estimate, and we obtain further new properties of these functions. Our analysis shows that these functions of Vladimirov are exactly the Hardy H 2 class of functions corresponding to the tube T C .