Choquet integrals, Hausdorff content and fractional operators

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,... Show more