  It is shown that the fractional integral operator $I_{\alpha}$, $0<\alpha<n$,
and the fractional maximal operator $M_{\alpha}$, $0\le\alpha<n$, are bounded
on weak Choquet spaces with respect to Hausdorff content. We also investigate
these operators on Choquet-Morrey spaces. These results are extensions of the
previous works due to Adams, Orobitg and Verdera, and Tang. The results for the
fractional integral operator $I_{\alpha}$ are essentially new.

Functional Analysis