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In this paper, norm estimates are obtained for the problem of minimal-normtangential interpolation by vector-valued analytic functions in weighted H^pspaces, expressed in terms of the Carleson constants of related scalarmeasures. Applications are given to the notion of p-controllability propertiesof linear semigroup systems and controllability by functions in certain Sobolevspaces.

Tangential interpolation in weighted vector-valued H^p spaces, with applications