The integration of functions in the weighted Hardy spaces

Analytic functions in Hardy space H^(s)(\psi\text, \!\!\!\!\Gamma) on tube domains are described. We prove that F(z)\in H^(s)(\psi\text, \!\!\!\!\Gamma)(2s \text＞ n) if and only if F(z) can be expressed as Fourier-Laplace transform of a function belonging to L_s'^2(\mathbbR^n) and is supported in set \overlineU(\psi\text, \!\!\!\!\Gamma). With s=1, relationships between spectral functions of F(z) in H^(1)(\psi\text, \!\!\!\!\Gamma) and its partial derivatives of one order \partial F(z)/\partial z_k for k\; \rmequals\;\rmto\;1\text, \!\!\!\!2\text, \!\!\!\!\cdot\cdot\cdot\text, \!\!\!\!n.