Some new tent spaces and duality theorems for fractional Carleson measures and Qα(Rn)

Several duality questions for fractional Carleson measures and the spaces Qα(Rn) are resolved using a new type of tent spaces. These tent spaces are defined in terms of Choquet integrals with respect to Hausdorff capacity. A predual for Qα(Rn) is then defined as a space of distributions containing the Hardy space H1, and an atomic decomposition is proved