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 α ∈ [−1/2, ∞) 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.

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