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This study investigates the restriction problem for the Riesz potentials of Hardy-Hausdorff spaces HH1-γ (Rn) and Q-type spaces Qγ (Rn).By exploiting a geometric-measure theory generated by the indicatorlike functions of compact sets,it is proved that the Riesz operator Iα continuously maps HH1-γ(Rn) into the weak Morrey spaces Lq,μ,λ* induced by a Radon measure μ,which obeys a geometric condition.