Choquet Integrals, Hausdorff Content and Fractional Operators

We show that the fractional integral operator Iα , 0<α <n , and the fractional maximal operator Mα , 0≤ α <n , are bounded on weak Choquet spaces with respect to Hausdorff content. We also investigate these operators on Choquet–Morrey spaces. The results for the fractional maximal operator M_α are extensions of the work of Tang [‘Choquet integrals, weighted Hausdorff content and maximal operators’, Georgian Math. J. 18 (3) (2011), 587–596] and earlier work of Adams and Orobitg and Verdera. The results for the fractional integral operator Iα are essentially new.