A class of subspaces of Morrey spaces and norm inequalities on Riesz potential operators

摘要

We introduce two classes of Banach spaces F(q, p, α) and T p, α (1 ≤ q ≤ α ≤ p ≤ ∞) which are subspaces of Herz spaces and Morrey spaces of functions and measures respectively. We study the Riesz potential operators in these spaces and obtain norm inequalities on these operators from which we deduce a necessary condition for a nonnegative Radon measure to have its Riesz potential in a given Lebesgue space.