  A method of proving Hardy's type inequality for orthogonal expansions is
presented in a rather general setting. Then sharp multi-dimensional Hardy's
inequality associated with the Laguerre functions of convolution type is proved
for type index $\al\in[-1/2,\infty)^d$. The case of the standard Laguerre
functions is also investigated. Moreover, the sharp analogues of Hardy's type
inequality involving $L^1$ norms in place of $H^1$ norms are obtained in both
settings.
